I, personally take offense to the term babysitter so I can understand that rubbin you the wrong way. At the same time, people who are NOT in this field do not understand how condescending that term can be and it's simply the word that they know to use. I wouldn't get too upset over being 10 min late..we've all been late before, especially going to a place we've never been to before. If they were 30 min late that's a whole different story!
I guess just go with your gut! See how it goes for a couple weeks, and if there are any more red flags...NEXT!!!