If it helps, my situation was that I'd been in Canada for more than six months (with legal temporary status) at the time we submitted our application, too. I was worried about the RCMP clearance, knowing it was supposed to take 120+ days to get results, but the application instructions said not to order one unless you're asked. All I could see was delays, delays, delays!
It turned out that they do an RCMP name check on you immediately after receiving your application, and if your name comes back with no "hits", you're good. If your name check
does produce a "hit", they will send you a letter asking that you get a fingerprint check done. With this letter you can go to an agency like
Commissionaires (and there's another that I can't think of the name of right now) and they can do a digital scan which sends results to CIC within 72 hours. Without that letter Commissionaires can only do a standard fingerprint clearance request - so the letter is important. But at least you know that, in that eventuality, it will not take 4 months to get results.
So - wait to hear from CIC and don't worry in the meantime.