Honestly - it is rare to find a painter (a good one?)that is willing to apply color coats over someone elses prep work. His name and reputation will be based on your prep work.
Again - my $0.02 - You really want to use the same brand of primers/sealers/top coat paint. They are engineered to be compatible. Everything I have read on painting says this is Painting 101 practice. I have painted 2 cars and I would not do it any other way. Time/material are too valuable to risk having compatibility issues.
I paint 300+ cars per year and disagree. We use different brands of primers/surfacers/sealers and different clear coats depending on the job. We have had ZERO problems with paint issues.