Parallels Internet access

I have set up the current version of Parallels on a Mac, and have it configured, and then set up a new, parent controlled account and opened up parallels to configure it for my child's use. Immediately parental control did exactly what it is supposed to do and informed me that parallels is attempting to access secure websites, and then ran through about 20 different IP's. I initially allowed it figuring that it was necessary for some sort of activation check. But then once I got in and opened an application and then closed it I received another notification that parallels is trying to access the internet.

What is parallels desktop trying do? Why is it tracking literally every application I close? Will these forever pester my child unless I permit? and if so what happens if I simply block?