Enamel paints (which encompass most spraypaints) often take quite awhile to fully cure. Depending on temperature and humidity, it can be as long as a week. Until then it tends to be slightly tacky.
Primer is generally designed to dry quickly, so that any category of paint may safely be applied overtop. I don't have any guess as to why this would be causing you problems.
I don't have direct experience with mod podge, but i was under the impression that it was basically a clear acrylic paint.
One possible solution would be to coat your armor with wax, such as Johnson's Paste wax. Unsurprisingly, it gives the surface a slightly waxy feeling, but it does improve the shine, and should act as a barrier from any sort of tackiness you might encounter. I can't make any promises, so you might want to test this on an inconspicuous area.
To apply, you simply brush on a thin layer with any sort of brush. Wait a moment for the solvents to evaporate, and then buff the excess by rubbing rapidly and lightly with a soft cloth (I like old t-shirts best for this). the rapid buffing slightly melts the wax and evens it out to a smooth layer. A second coat is only needed if you don't feel like you covered the entire surface.
Another emergency solution to remove tackiness is to coat the surface with talcum powder. I get mine from my local pharmacy (I've even used foot powder in a pinch). However, this can cloud the appearance of your finish and lower the gloss. You dust the powder on in excess, brush it around with a long soft bristled brush, and then whisk off the excess. If you want to risk it, you can try blotting off additional excess with an ever so slightly damp paper towel, but this risks restoring the tackiness, depending on the nature of the sticky. Oh and you should probably wear a dust mask during application.