What you are describing is typical for some preschool children that age. If the teachers are handling it properly, and yes, letting her cry for a few minutes until she calms down is ok, then she will eventually stop.
In my many years as a preschool teacher I have always given the child some time to get their feelings out before I intervene. I would then offer them a choice of an activity to do to give them some control. If they decline, I allow them to stay where they are and observe our morning routine from a distance. Usually within one week of this the crying stops because we had lots of fun in my class.
And yes, crying is contagious, at that age especially. When one starts, another will start, and another. If you trust your daughter's teachers, trust that they have the experience to handle the situation. This transition is really harder on parents than it is on kids.