I understand the general premise but I wouldn't venture to say that I understand this completely (didn't read the references).

So if the DNA is found outside the nucleus in the cytoplasm then STING is indirectly activated. In turn it activates the immune system as a response to the viral infection.

The activity of STING is targeted and lowered by some types of viruses and cancer cells and thus giving the advantage for their propagation without our immune system ever getting to know about it, maybe until much later.