Primer is truly one of the most misunderstood products in the car industry.
Epoxy primer is the only one I can think of which would have protected you & it seems like you got something less.
With reams of information available on the topic of primer, I won't waste time here...the answers are at your fingertips for those who think the base upon which your entire body & paint will adhere is important.
The part which I'd like to explain is about the rusty seam at the rain gutter. NO amount of media blasting with remove the rust sandwiched between metal panels...such as the rain gutter. It simply can't.
Unless you drill out the spots welds & grind it away....or can somehow flush enough acids through the tight areas and thus rid the rust and hopefully convert any remaining traces to a stable compound...it stays there forever, to re-emerge with the slightest hint of moisture unless it's encapsulated someow and kept dry.
After the above mentioned it should have epoxy primer flowed into the seams then propelled deeper with a blow gun. To further ensure the rust doesn't creep out, one could apply a good quality, thin seam sealer to further ensure any rust traces stay buried.
Meanwhile back at the primer... Soft porous primers will absorb water like a sponge and hold it against the metal...ATTRACTING moisture even and creating rust. I recently learned of a fella finishing his primered car for paint... by wetsanding. That's a very risky move and a basic understanding of primers will make it clear that the absorbed water from sanding could very possiblely make the final paint blister as rust grows from pores and/or trapped moisture tries to escape.
Mitch you are lucky at least to have noticed it at an early stage and now have a chance to restrip it & use a correct product.
Did not the media blaster fella warn you the primer isn't waterproof? Maybe you guys could reach a deal where he blasts off the garbage primer and you supply some epoxy?
I'd maybe consider doing some research on this important step & also try to stick with the same product line from primer to paint. In other words choose you paint brand NOW and use the directions and products they outline in their instruction sheet. As already mentioned, etch or washing acids with phosphoric content play an important role to prep your metal for primer. The instructions vary with different acid products and must be adhered to closely to ensure close adhesion...(pun intended)
For what it's worth... I've worked over a dozen years in a body shop fixing & painting (and guaranteeing) rusty cars.
...and now 19 years & counting in my autoglass business, dealing with rust around hundreds of windshields each year. Please understand I'm not bragging, in fact ANYTHING to do with fixing rust is just a dirty, messy, demanding job that puts one in constant contact with nasty chemicals and toxic mists & dust.
Hence it just doesn't make sense doing the job twice.