Is it normal for a yoyo to tip over on a simple trapeze?

If you do it wrong, yes.

When I learned trapeze, the Yo-Yo would either fall off the string, snag the string and wind up, or miss the string entirely. After a lot of practice, I stopped running into these problems.

This is the exact video that helped me with Yo-Yo tilting when I was learning:

Basically, work on starting with a good throw, then focus on keeping the strings all straight on the same plane.

Lighter and less stable yoyos may be more susceptible to this, but it’s really a practice thing.