If your dog was treated for heartworm and cured, the tests now are just to be sure and certainly should NOT show any heartworms - you are misunderstanding something, either he wasn't treated fully or he is reinfected.

As long as your dog was cured and is on monthly heartworm preventative, he should be heartworm free.

To be specific, there have been cases of heartworm occuring in dogs on preventative, mostly in the New Orleans area - seem some heartworm do not get blocked by the normal preventatives, but that is very rare.   You need to get a better answer from your vet - or you did not understand what the "cure" was.   The preventative does not cure - it prevents, if your dog had heartworm already, the cure is a 3 stage, rather expensive treatment.