I have 4 character-specific favs but it will only work with the one I most recently favorited. I un-favorited Death Seeker, then favorited it and then that pet was doing the same thing seen in the screenshot. The 4 character-specific favs are also global favs. I also tried summoning them with action bar buttons, but they still just get replaced with Chompy if I do "/petwalker n"

Are you sure you don't have any filters set in the Pet Journal, or text in its search box? (e.g. "chompy")

The "only eligible random pet Chompy" message points in that direction. See also This section of the FAQ and Answer to Issue 6. Note that the filters / search box of the Pet Journal are relevant, not the ones of Rematch.

As an aside:

I do "/petwalker n"

You could also do /pw n, or does the /pw command conflict for you with another addon? You can also set up a key bind for "new pet" in the usual key bind section of the game settings.

aha! that fixed it. I hadn't cleared the search box. Sorry!