I suggest you look at this a bit differently. It sounds to me like this is a task you're willing to do and recognize the value of, but you also want recognition that you're going above and beyond your official job duties, and you want some control over when and how often you do it. For that, it doesn't matter whether it's technically tutoring or collaboration (probably it's a bit of both anyway). What really matters is making your manager aware, setting expectations, and ensuring they will back you up if you need to set boundaries on how much and when you mentor this person. Hopefully you and your manager regularly have one-on-ones, but if not, now would be a good time to schedule one.
When you talk to your manager, tell them you are getting these requests and that you're happy to help mentor a new employee, but you'd like to know how to prioritize it among your other work and how much time you're expected to spend on it. It's your manager's job to prioritize your work, so let them do it. If you have a preference for what answer you'd like (such as "I think two hours a week is a good amount, with occasional weeks off at my discretion if I get overwhelmed with other things"), then suggest it. Chances are if you have a suggestion ready to go, they will agree to it.
This approach accomplishes multiple things that seem to be important to you:
- You get recognition from your manager for mentoring the new employee, which is more important than recognition from the new employee
- Assuming you get permission to decline these meetings at your discretion, you will then be able to do so without worrying about blowback or being seen as not a team player
- If the new employee starts demanding more of your time, you can blame your manager and say you've been directed to spend the extra time on other tasks
- As a bonus, you'll have dedicated time to spend on this instead of having to explain delays on other tasks because you decided to do something nobody told you to do
If your complaint is more about your colleague setting up meetings at times that are inconvenient for you, then simply respond to the meeting request that it's not a good time for you and suggest a few alternatives. This is completely normal in a professional workplace, so nobody will be offended by it. Another option is to be proactive and set up regular meetings at a time and cadence which works for you.
Source: I'm a software developer in a large company, and I've mentored several new employees. I didn't used to talk to my manager about it, but now I always do, and things work much more smoothly for me now. My manager is generally hands-off, but setting expectations and making them aware of what I'm doing has still benefited me. I also set up regular meetings with the new employees on days and times that work well for me, which limits interruptions to my other work at inopportune times. I sometimes cancel or move those meetings, and it's never been an issue.