Whoever told you this lied to you. You don't apply for Quebec until the federal government asks you to do it
The process is: apply for sponsorship to the federal government, get AOR1, later get Sponsor Approval, then you get an additional letter indicating that the file has been transferred to a local visa office (AOR2) and in that letter they invite you to submit an application to your provincial government, it's at this point when you apply to Quebec. It could easily be 6 to 12 months after AOR1 so don't stress about it, sponsoring a parent is according to the website a 20 to 24 months process so it's not fast and a lot of patience is required...
Hope this solves your doubt