daycare accidents

Hello I am actually a nanny (ttc), this question if for my boss. We have him completely trained at home. We started 2 weeks before he started with daycare (he was there over the summer). He is school from 9:30 - 12:30 and he can't seem to not have accidents (1-3) in that time. The daycare suggested pull ups. We feel that it not going to help but make things worse for when he is with us. He is shy so there are so many factors on why the accidents but we don't think pulls up are the answer. It has been a month since school started and it has been the same everyday. I know the teachers are frustrated and have other kids to take care of. I guees what we are asking does anyone have a different solution or in the same situation? Please help. Thank you in advance.