So are the 6x6s attaching just into the plywood or are they going into something behind the plywood? Overall it sounds fine what he told you to do, but what they're attaching to and how you do what we call "blocking" to secure them is how you determine if you can hang cabinets.
Edit: Per your additional information, what you're doing is fine but I'd ask him specifically about where you want to hang cabinets because you'd need to make more consideration. They put a lot more strain than thin drywall to the fasteners that are holding them up.