When you want to improve your turns you’ll need to strenghten you hip and thigh flexor muscles or your Pectineus, Sartrorius muscles, Gastrocnemius and the Soleus (they’re crucial in jumping). There are a lot of plyometric exercises along with squats, lunges, and bounding exercises that will also help you. Here’s a list of other exercises that can help you get you or your swimmers off the wall faster and farther.
Don't do things that hurt. Pain and potential injury usually occurs when you do the exercises incorrectly. You don't have to do things that hurt you to get off the walls better. Find and exercise that you like and slowly increase stress to improve.
Bounding
Lunges
Deep Knee Bends
Deep Knee Bend Jumps
Toe Raises
Toe-Raise with Weights
Jumping Rope
The entire foot is on the wall so the swimmers can recruit as much muscle as possible.
Phelps entire foot on the wall.
YouTube - Michael Phelps turn
At :48 seconds, you'll clearly see Natalie Coughlin push-off the wall with flat feet.
YouTube - Natalie Coughlin Swim Tip #5: Flip Turn
Aaron Peirsol's collapses to a flat foot on his second backstroke turn (a little hard to see) but it happens.
YouTube - Aaron Peirsol 200m Backstroke
Breaststrokers like all swimmers collapse from the balls of their feet to a flat foot. YouTube - Brendan Hansen Men's 200m Breastroke
Good luck, Coach T.