I think it depends on the content of your paper. If your own publication has nothing to do with the tutor's research, there is certainly no need to discuss it. But if your thesis is related to your tutor's research, or if you have been instructed by your tutor, then I think you must tell your tutor about it.
And I think if this is the kind of thesis that you sent to get the qualification of degree defense, please be sure to confirm it with your tutor. Accept his suggestion, including the order of names and publications to be submitted. Especially before submission, because your tutor is definitely more experienced than you, your tutor's submission will definitely improve the quality of your paper.
One more thing, I think people should keep a modest learning attitude. After all, the mentor is your mentor. As a student, I think we should communicate with your tutor frequently, so as to enhance the relationship between you and learn from your tutor. I think this is also an important part of interpersonal communication.
So as I wrote above, it depends on whether graduate students must consult with their tutors when publishing their papers. Personally, I think it is better to discuss with the tutor whether it is related to the tutor's research, mainly because I can learn a lot from it and listen to the opinions of many tutors. I think this is still necessary.