These critters definitely move into new areas.
I live on Wrangell island in SE Alaska.
About 15 years ago, there were sightings of an unusual animal with a long tail by children in the school playground. Not much more was thought about it until shortly after, when a fellow who lives outside of town came in by boat and put a dead mountain lion on the bar in the saloon.
He was later charged by Alaska Fish & Game with taking an animal out of season, and was convicted because since we don't have mountain lions in Southeast Alaska, we don't have a hunting season for them either. It was found to be full of deer meat.
The lion was confiscated and after the trial it was given to the school. They had it mounted and display it at the school in a glass case as their mascot, and call their ball team the Cougars. Since that time, there has been one other lion caught in a trap, and a few others seen, some with photographs.
But officially, we still don't have mountain lions here.
I have not seen deer in trees, but that might be next.