When I worked in a center all of our fees for training were paid for by the center itself. The trainings were also chosen by the center-so no "Pandora's box" so to speak Often times to keep the trainings affordable our director would hire someone she know to come in and do a class for all of us at once. For example: She brought someone in to teach us all our first aid/cpr classes. If we could not attend that class we still needed to be certified but had to do it and pay for it on our own.
We were not paid extra for this, it was part of our salary. I guess if we were hourly then we would have had to have been paid.
There was education I was required to have in order to be hired in the first place (bachelors degree) and of course I was on my own for that
I'm not sure about the legalities of this-but it makes good business sense to pay for the required trainings for employees.