Hi, I noticed this exact same problem last week. I was going to make a post about it here, but you saved me the trouble.
This looks like a bug to me. To clarify for the devs: if you use form logic to make a button visible, the button will become visible on whichever tab you are currently on when the form logic rule gets executed, even if that is not the tab that the button is on. Only after you switch to the actual tab that the button is on, does the behaviour return to normal, ie. after that it is no longer visible on other tabs.