Maybe this is easier for me to understand as I've not followed the cartoon series and never really liked GB2, but they way the comic works seems very straight forward to me.
Y'know, when reading it, I wouldn't even take the fist movie into account. The Ghostbusters comic story starts at Legion #1, not the movie. The events of the movie did happen, but you don't need to know them. Anything you need to know from the movie gets explained in the issues and you can enjoy it without any knowledge of the film.
In the film, at no point does it say “hey, this is 1984!”. You can tell from the fashions and the overall 80'sness of it all, but it's not part of the story. The movie has aged extremely well and, if it was released exactly as it was today, it'd only be the fashions that give anything away.