With regard to the Supergirl series, I've seen some complaints on other sites about how her episode was a just red skies story (referring back to the comics - many issues would feature the Crisis on Infinte Earths Crossover banner, but the story inside had nothing to do with Crisis except that the sky turned red). However, I think this Arrowverse crossover will have more impact on Supergirl than any other series.
In the Invasion era comics, Mon'el had a significant tie to the Dominators; it was his father's sacrifice in protecting people from the Dominator's that inspired Mon'el to become a hero. Mon'el would later beat back a second Dominator Invasion and seed their metahuman experiments on various worlds so that the Dominators couldn't find them again. That act would lead to the United Planets and eventually the foundation for the Legion a thousand years from now.
I believe the aliens looking for Mon'el are also Dominators. And at the end of this crossover, Supergirl is either knowingly or unknowingly bring something back that emits a signal leading the Dominators of her reality to her earth.
Incidentally, the comics version of the Dominator Invasion led to Snapper Carr being abducted and getting powers (the ability to teleport with the snap of his fingers).
