I dont know the answer on the OBC from OTA as I have not booked a cruise with OTA since 2004 or 2005. Since then we have found a great cruise agent thru referral (she did not take new customers at the time unless being referred by someone she knew.)
I used to check prices on possible cruises on Cruise-n-More before the site changed to its current form. Nowadays I use Vacationtogo to check prices then email our cruise agent about the cruises I am looking at. Being the top agent of all mass market lines she will have the same pricing as Vacationtogo, and sometimes has other incentives that she can pass on. My experiences have been Vacationtogo probably has the most competitive advertised pricing, plus it also tells you if there are special discounts for returned passengers. The only quirk with Vacationtogo is it does not show the amount of taxes and fees - that can be very substantial in some itineraries.

The Celebrity cruise I booked had a $50 OBC for the cabin but I did not know where that came from as the rep never mentioned there was an OBC.

It was when I looked at the booking on Celebrity website, it said I had $50 credit that I could use to pay for excursions or drink packages etc online before sailing. I did not do anything and the OBC stayed in the shipboard account and offset the total shipboard expenses.