Argh... I must say, I totally feel with you on this.
This kind of personality Tom has is the most toxic one an aspie can have in their surrounding. I faced such people in my past a few times already1. And it doesn't really matter what is the best way to give such an apology.
I would advice you for the current situation to simply apologize any inconvenience your interactions have caused and point out that you didn't intend to blame him for anything and if you appeared to do so, apologize for that as well.
That's all you should do for now. Likely he won't believe you and just assume, you're trying to retain face, but there is nothing more you should do, as any more info about why you did what you did, or attempts to explain your actions will be understood as attempts to justify and defend your motive.
The reason for it lays on the four-sides model established by Friedmann Schulz von Thun.
The problem here is, autists, contrary to allists have their communication2 based on the sides of self-revelation and factual information. That means autists usually intuitively try to transport information about their own condition (i.e. How they feel) or about how things they want to talk about are factual perceived by them. And also that's the main information an autist usually intuitive abstracts from a message they received. Ironically for an allist it's the exact 2 other sides they usually communicate through. It is the appeal- and the relationship- side they communicate on. So they understand and express in the subtext of exchanged messages how one evaluates the relation to the other and also express their expectations how you have to act and what you have to do(an hidden Appeal), and vise versa, also allists usually assume the messages they receive are on these 2 sides so understanding a lot of Factual information like
I need Help, I am dying!
as an appeal that they are obligate to intervene. While it for you most likely was just meant as an factual information --> You are about to die, if no one is able to intervene immediate, its to be expected that you will be dead soon.
And that's the main problem here both of you heard and said the very same thing. But you two communicated on different sides of that model.
So when ever you come up with this situation again, he will just take it as you coming up with that situation where you had made an appeal and he wasn't able to achieve what you (apparently) expected from him. Hence its for him like you are just trying to display his failure again....
Usually these interactions between autists and allists cause inconvenience once or twice, maybe even trice but as it is in our autistic nature, since we communicate on the self-reveal side we tempt to explain our selves. How a previous situation was meant, what our intentions had been, that we meant literally(factual) what we said and that we are sincerely sorry if we made someone feel uncomfortable with what was said.
After that, at least open minded people take that for the future into consideration, and even those who lack the intelligence to understand it or the tolerance to accept difference, they still treat the new information in some way to act accordingly.
But in my life so far, it happened 4 or 5 times3 to me that I met someone behaving the exact same way as Tom does. I think this must be due to some psychological condition4, as the behavior and the reasoning behind it was identical as far I could observe it and there are easy calculable patterns I found for myself to identify such a personality early on (I won't share them, though. Since it's just layman knowledge and if I'm wrong, my observations could cause more harm than help.).
With the previous in mind focusing again on How can I apologize to coworker while avoiding another lecture?
So for how to approach Tom (assuming you have a relative close relation to him, given you have mutual after work activities), you could try to introduce the four-sides model to him explain him, that you understand how he perceived that message and explain him at hand of the factual information side, how you meant that message instead. Most likely he will understand it.
But be careful. If he is in fact an unsafe person he will just pretend to have understood... Or in fact have understood but later on just disregard it again. And you will just end up in similar situations again.
So considering that, I would rather like to provide you an frame challenge to prevent you from coming up yourself with what I just figured painfully over the years.
I wouldn't even advice you going any further than a simple apology. Since he is a work colleague of yours and just testing if it solves the problem or you will just end up in a similar situation again might end up having a really uncomfortable time at work in the future.
So I would advice skipping that part with the deep self-revealing explanation and just avoid him as much as you can. Reduce your interactions to only work related things and hold any communication on the self-reveal side at a minimum, just communicate factual information to give no opportunity for misunderstandings.
Now a little explanation about the term unsafe people I used before.
How Tom can be most likely be considered as such and how they are a source of stress to our lives (especially for autists). The Problem here is, it isn't about being wrong or right. Actually both of you are right. Because there simply is a mismatch in the protocol being used for communications. One thing I learned by the linked blog post was: It matters most if someone isn't good for me, not how well their intentions are. You can't blame someone for that, but that doesn't mean you have to bear it.
The fact alone that someone isn't good for me is actually the most important thing for me in deciding to not pursue any further contact or at least limit it very strongly. One thing I kept reminding my self after having read that blogpost was being aware, some people don't mean it bad nor even have bad intentions... but they simply aren't good for me because they don't fit to the personality traits and social requirements an autist has.
I wrote down the red flags, signaling to me that someone seems to not be a safe person and started actively avoiding them as soon these red flags are being raised too often or just too many of them. I pinned the on paper written flags inside of my flats exit door, so I remind my self every time I leave the flat, that I want to watch out for these personality traits and want to avoid them.
And even while being aware of this, it was quite a few times very hard for me to cut loose someone I really liked. But the flags clearly indicated, that person won't be good for me on the long run. In the end it was rewarding!
I can say that currently there are just safe people in my close social circle, and it is so much less stress, I can be so much more open and less considered how to act when being with them as they fit to me and don't cause any discomfort, be it unintended or intended by them. So I really can just advice you taking these considerations into account for future Toms you might meet, before letting them enter your private life too deeply.
1 I.e. that famous coworker I asked for help about in this post: How to have a talk with a coworker I'm scared of?
2 Means, the intuitively transported subtext expressing the means of a message you sent and also interpretation of the subtext of a message you receive. Verbally, digital or through what ever medium.
3 4 times for sure, the 5th time I had not the interpersonal skills I have now, so looking back at it, it is hard to say if there was a number 5 or it was just me interpersonally failing in that situation.
4 Disclaimer: This is my personal conclusion and hence just an assumption. I have literally no data to back that claim up except from my own logical sense and my layman psychologics knowledge.