There are differences between the Provinces and their connection to you.
Example:
http://gyazo.com/749483923f570f3854f2a9535e5bc0db
"Grenoble" is a province of mine after capturing it from france. So at the beginning it was part of France and now it is under my control. It will just produce 25%. Cause of the people living there feel connected to France and not to me cause of the historybackground. The province is categorized as core province. When France would capture it back from me the production in the province will be on 100% output again.
"Sfax" in the south is a normal province without a connection as beeing a core province of a selected countrie. Also we just have a production of 25% maximum ressources output but all countries will just get these 25% cause of it beeing a "colony" of france or the owner at the moment.
To give you a clear answer after all:
Yes every province which is not categorized as core province of your countrie will give you just 25% of its production. This makes it much more harder to protect your new owned province against enemys when you grow to fast or so.
