J.S.
I doubt very highly that there's a problem with this sub. I think that your son is reacting to the fact that it's not his usual teacher. She looks different, she sounds different, she does things differently. As much as she may try to stick to the same routine it's just not the same. It's a major wrench thrown in the kids' day. Some children handle it better than others. Some are more sensitive to the changes and more anxious about it.
I would bet that if your husband wears a beard and he suddenly shaved it, your son would behave the same way around your husband.
I wouldn't worry. If it continues to be a problem, be reassuring but also listen to your instincts and pay attention to how the other children are behaving. I think it's a very good sign that he does allow you to leave and when you check up on him he's happy and having fun.