To be honest I had that concern when he moved from Hibs to Villa because of the pace of the championship. I thought he might struggle but he made the league his own.
One thing that must be clear to you Villian's now is that the laddie doesn't know when he's beat. He never gives up. Never shies away and even on a poorer performance (distribution wise) he gives everything he has disrupting the opposition. His willingness to literally put his arse on the line combined with his skill as a footballer results in him making his own luck, shown in both goals in the final.
When you have a player in your team with that mentality, I wouldn't worry IF he'll adjust - only how quickly he will.
All the best in the Prem!