Do not let your caregiver freak you out. There is absolutely nothing wrong with your child. You have not done anything wrong, or led your son down "the wrong path."
A 19-month old baby cannot be a bully. Your son is becoming fully aware of the world around him -- and is beginning to learn how to reach out and take what he wants. He has absolutely no understanding that other people have feelings. In fact, he doesn't even understand cause and effect (that his actions can cause something else to happen). Your son's entire world is becoming about him and his wants. Welcome to the "terrible twos!"
Yes, this is the appropriate time for you and your childcare provider to start teaching him that "we don't take things from other people's hands." However, at 19 months old, he will not be able to easily comply -- let alone self-monitor himself! Further, at this age, he is too young for punishments. You and your childcare provider should be using distraction and redirection with him. And, if your childcare provider does not understand this concept, you may want to consider finding a new one.
Try to get a hold of the book, "Discipline-The Brazelton Way" by T. Berry Brazelton, MD. It focuses on discipline for age 0-6yrs. At this age, discipline involves teaching (not punishment), and providing boundaries that all kids require. And get a copy for your caregiver. I think she needs to lighten up.