This is an old thread now, but just in case somebody else comes across it. I have experienced this on my Bartletts Anthias before. Its eye was popping out and it was hiding in a cave for a week. In my tank, I think it got pop eye from bumping into a rock or something which scratched the eye and got infected. My water conditions were pristine. I say leave it in the main tank, don't stress it out by catching it and putting it in a new tank. IMO
that will only make things worse. Make sure you water parameters are pristine condition and just keep feeding healthy and wait. It should clear up on its own. My Bartletts did clear up and I though for sure he would be a goner.