Hello, I'm not going to be able to tell you the answer, but as you need to be sure about it, I think the only thing you can do is ask them directly. The studentship could be implied by your being assigned to the subject, and maybe they are covering the tuition fees, but as they don't say that anywhere (based on what you've said), I think that you need to go back to the department/research centre and ask if the assignment means that you have been awarded the studentship.
I hope I haven't misunderstood your situation - please post back if I have and I will try to help :)