No real time update of Avatar in Desktop vs Phone and no update on posts/comments

What I was trying to do:

Changing my Avatar in Desktop does not update the Avatar on Desktop

What I expected to happen:

To have this updated real time in all platform/environment (Airside/Resident/Citycare) and having this updating my old posts/comments with my new Avatar.

What actually happened:

I see an update in phone web (which is weird) but not in Desktop. After, if I update from the desktop, no appear on the phone. But if I change from the phone, the change appear on the phone, but it finally update on the desktop when I reload, but the image not the same in my profile vs the top right icon...something is not right here....