does he twitch only when the mouse is in the container? if so, nothing to worry about.

if he's twitching all the time and it's recently started, sounds like a problem.

any exposure to extreme heat or cold? any chemicals sprayed near your home for pests or weeds? sprayed any new air freshener type products in your home?

if anything like that has happened... vet asap imo.

hopefully FR or Bluerosy will chime in soon as they have much more experience than me.