Yeah, the anime wasn't the clearest in this regard. Since you already watched season 1, I don't feel bad writing out the explanations below, but for those that haven't seen the series yet; spoilers ahead.

Basically, Cid made up the Cult of Diabolos as a cool sounding story when he explained it to Alpha as a child. In the scene you see him grab a book and look at a bottle label. These were inspiration for the story he was making up. Specifically, there is a legend in the world of heroes that slayed the great demon Diabolos and saved humanity. Think of this legend similar to tales of the city of Troy is in our world. Achilles, Hector, etc. are mythical figures much like the heroes (like Olivier) are in that world. He made up this story featuring elements of the mythology around him because he thought it sounded cool (who wouldn't want blood of the heroes running through their veins).

What Cid didn't (still doesn't, and likely never will) realize is that there is an actual Cult of Diabolos that has exerted its influence in the background of society for ages. They conduct research on what remains of Diabolos (revealed to be Aurora the Witch of Calamity) to try to extract its power (eg. the red pills Grease and Zenon use to power up) or extend their life (the drops that the Knights of Round use). The cult uses the church as a means to gather and experiment with/exterminate all the people that show signs of possession. These individuals are the ones with the most active expression of heroes blood. Basically, possession is the result of the magically powerful heroes blood running out of control with magical energy so that the host body can't control it. When Cid or the girls cure someone of possession, it is rewriting the way their body controls magic to be able to fully harness all of that magical potential. This is one of the reasons why the Shadow Garden girls are so powerful.

So, to recap, Cid told Alpha that Diabolos placed a curse on the heroes so that their descendants suffer from possession while the Cult then experiments/disposes of the possessed. He was essentially correct, but the "curse" that Diabolos placed on the heroes was actually a result of the Cult itself experimenting with implanting Diabolos' cells in children, creating the heroes.