Well they are a team on the rise. Let's just say they're following the same steps as other teams who've set serious targets such as promotion to Serie A.
For example Chievo were in C, promoted to B and eventually made it to A in successive promotions. Palermo most recently have been following this example.
Some teams were similarly on the rise from C to A, but simply plunged downwards like Padova, and Salernitana.
Rimini were in Serie C 2 seasons ago, and won it, then in 2005/2006 finished in 17th, enjoying a few good results here and there. Obviously their main aim was survival in B...now I think they're probably fighting for another year of survival since their squad on paper doesn't look like one of a serious promotion contender.
That said, anything can happen in football...so you never know.