There is no single answer. Every MOC operates on his/her own timeframe. The only requirement is to submit the nom slate to the SAs by Jan. 31 or, for those leaving office, by Jan. 21. Whether the MOC does it in October or on Jan. 31 is his/her call.
Also, the fact that an MOC has told you that you have a nom doesn't mean he/she has submitted the slate to the respective SA. Once the SA gets the nom, if you are triple Q'ed and have an LOA or are the principal nominee, it generally takes a couple of weeks to get the BFE.
And to answer your question, MOCs typically submit a slate all at once. If they don't have enough applicants, they may wait until the last minute and accept additional applications (THEY can change their deadlines, YOU can't). If they are like most MOCs and have more than enough applicants for their 10 spots, they typically have a selection process that may or may not include interviews. How long it lasts depends on how they go about it.