I just paid the fee and upload the documents following the reminder email.
You're right. RFPF usually comes later than the MR, or at the same time. I guess paying RPRF and update the file now (same as upfront RPRF payment when submitting the paper documents) may accelerate the final procedure a a little bit (10 days).
For CIC themselves, it's about the accrued interests on their balance. Considering the whole application is about 16 months, it actually has some impact on CIC's total interest income.