If a Pokemon uses U-Turn, switches out, and new Pokemon comes in, and the opponent uses Counter, will the Pokemon that just switched in take damage? It didn't deal the physical attack, sooo....
Same goes for Volt Switch and Mirror Coat.
If the last physical attack to hit the user was from an opposing Pokémon, this attack deals double the damage done to that Pokémon. Does not affect Ghosts, but hits everything else for the same damage.
-Smogon
So regardless if they switched using U-Turn, the new pokemon will get dealt double the damage the U-Turner did.