We dont' get up till we have rested so having to stay on their cot for another 10-15 mintues or whatever you feel works for your program can sometimes work in the sense that the next day he is reminded about the consequences of not resting when the others do. You may need to use a timer with him as in he must rest for a certain time and the timer restarts every time you have to speak to him about not resting quietly.

Find out from the parents what he did previously as in was he expected to sleep in his other program or at home. At 3 whatever he is used to doing is ingrained now and it will take time to change the routine and him to adapt., However he is old enough to make the change and know that you mean what you say. He may just need less sleep than the others. My own kids never napped in the daytime past about 18 months but they slept 12-14 hours overnight since I didn't have to wake them early in the morning to go to daycare. I loved having that time with just my own kids while daycare kids slept.