How adequate is this priming job?
You don't need to use primer on a previously painted surface that is properly prepared, unless there is some problem with the surface that makes you concerned about inadequate adhesion. 

Buy good quality paint with high white pigment (titanium dioxide) content and you will be (or would have been) fine. Apply 2 coats of paint if it doesn't cover for some reason (like poor technique or wrong applicator). What is this obsession with primer, do people just like to spend more money??