Recently, I've encountered a pop-up reminder from tixati: "Reminder... click here to donate". The problem with it is that the popup jumps at inconvenient times.

My question is - if I donate, will the reminder stop from popping up/go away?

everybody gets that reminder.

there is no way for the program to know that you donated, so even when you donate, you will still get the reminder.

the devs always need donations as they are constantly developing tixati.

Anyway to disable it?

They are non-intrusive, incredibly rare (around once in 2 months), and seem to only pop-up when Tixati's window is in focus.
Even if there was an option to turn it off, it would take more time to set that then clicking the "Ok" button on all the pop-ups i got within the last 2 years.

It does not pop-up if Tixati window is closed/minimized. I do not know of a way to disable it, I've never been bothered by it.