Does it really matter if you have given everyone full time contracts anyway?
Admittedly I've found in past versions that whilst I manage to get my entire playing staff onto F/T contracts it is impossible to get any of my staff to do so until the whole club turns officially professional.
This transition from semi-pro to professional needs to be done by the manager?
Not really, unless you mean by getting the team promoted. You don't have to have all prof. contracts or even any, when you get to League Two you will automatically turn pro.