Is this violation of academic integrity if I ask a question on Github public repository and post it as an issue?
It seems like you have to have a conversation with your adviser. There is certainly nothing wrong with your approach: You read through code on which you have knowledge and something to say; you then were proactive and wanted to fix the issue; all of these are commendable. If you happen to have been mistaken, well, that happens -- but then that's what patch review is there for.
So the stance of your adviser -- as you describe it -- doesn't make any sense to me or probably anyone here. That leaves two interpretations:
- Your adviser really has awkward ideas of what is appropriate or not on GitHub.
- You misunderstand what your adviser was trying to get at.
Option 1 seems unlikely, so option 2 seems like a distinct possibility to me. It's also one that can easily be addressed: Have a conversation about the issue in which you state that you are confused why the behavior was considered wrong, and ask your adviser to help you think it through.
Update: Following the addition to the original post about the conversation with the adviser, it does seem to me that option 1 above (that the adviser is a moron), however unlikely a priori, is in fact true. That's regrettable because in my fifteen years as a professor, I've never come across a situation where this kind of behavior by a professor would have been appropriate or, in fact, useful or warranted.
But, since I've been developing open-source software for more than 25 years now and have been leading open source communities for 20, I do think that it's worthwhile pointing out that the behavior of the maintainer of the GitHub repository is entirely reasonable and appropriate: We all value contributions from the general scientific community, and for all projects I know of (a substantial number), that includes cases where the person proposing a patch may in fact have been mistaken. So I continue to think that you did the right thing, and I do think that the response of the GitHub repository maintainer was reasonable and common. In other words, the behavior of the academic adviser really makes no sense to me. If I were to receive an email from someone's professor saying that their student had behaved inappropriately and suggesting that I block them from my repositories, I would certain (i) not do so, and (ii) be quite clear about the fact that I thought the student did the right thing and that the adviser is in the wrong and behaving in ways that make no sense to me. It is certainly no adviser's business to restrict what students post on the internet as long as it is in good faith and doesn't slander the adviser or university.
Given this adviser's stance, I am a bit at a loss as to what to suggest. Reasonable people are amenable to conversations, but apparently this person is not reasonable. Given that you have a job offer from elsewhere, the right choice may simply be to decide that it's not worth your mental energy to fight this fight. Or, you could talk to the department head or another trusted professor in the department -- what they will do is a separate matter, and it may not yield any outcomes that can still help you in the time before you graduate.
These days I see myself as useless and miserable person that just works more than 12 hours per day and the other 12 hours that I suppose to rest or sleep still I'm thinking about my research but I'm not happy, I don't have any friends, I'm depressed, I'm nervous, I'm stressful, etc. So, yeah I'm angry that people hates me if even I tell them the truth.
It sounds like you're going through a rough time. Grad school is stressful even in the best circumstances, and yours aren't the best right now. Seek professional help from a psychologist or similar professional ASAP. Your mental health is your first priority!
As of the original issue my two cents would be to make sure they mean what you think they do, as suggested in the other answers. If this is certainly their stance you need to find a new adviser. This person could be bullying you over nonsense for whatever reason. Get out.
I don't see any integrity issues. Your intentions seemed to be to correct an error. Unless your intention was to sabotage your competition, there is nothing wrong with this.
Possibily, your mentor believes you should have checked with others first, but acting rashly is not academic dishonesty.