I was wondering would you submit yourself on the IMDB board for a particular film if you actually read (against) other actors during auditions or would you let the production company do it (I noticed that they didn't put the casting people on it yet), they haven't put the casting director on the board yet, but it was mainly the producers/director that were the casting people?

NO! It's not a credited position and you're going to look stupid with Reader (uncredited) on your imdb profile.

And yes, it's the producer and director that ultimately hires. Maybe they were cheap and didn't hire a casting director.

It was a low budgwt SAG-Aftra film.

A reader is not a member of the production staff, regardless of whether you were hired by the casting office or the producer.