Some days ago I got one in the middle of combat. I usually drop the items I'm holding when I try to close the screen, including on water. The pop-up alarm also breaks the immersion of exploring quietly and just listening to ambient sounds.
My suggestion is to substitute pop-ups for entries in your experience journal. When you receive an experience, you would just get a marker on your screen - which therefore would not disrupt your other tasks -, but you could click on it later and see what it was.
The journal part is there because I don't think people care to read pop-ups right now. I believe this is mostly because XP messages are, currently, just an annoyance that has to closed as quickly as possible, so they don't read them. By putting them in a journal some of us would actually pay them the attention they deserve. I don't think many of us even noticed the new experiences.
Also, please increase pop-up/journal entry font size.