If they're permanently down, just spread them wall to wall. They're awful easy to trim.
On the other hand, is this an actual problem, or just one you're anticipating? We have puzzle mats but don't put them out all the time. When they're out, they don't move. They're textured, which gives good traction. Plus the 4x4 square mat is pretty heavy. I can't say I've ever noticed ours moving.