I noticed that that if I keep the ODI under 20% there are no base attacks nor haven attacks. If it's above 20% and going up (I abandoned my 1st campaign when ODI was at 46%) there are haven attacks everywhere, it was at least, for me.
ODI is generated in two ways:
1. Each time Haven fall ODI goes up permanently.
2. Each time Pandoran Nest/Lair/Citadel spawns ODI goes up temporarily. By destroying that Nest/Lair/Citadel you revert ODI to what is was before the spawn.
You didn't have any attacks at ODI under 20% because you killed all the Pandoran bases. But new ones spawn periodically.
I didn't know about the number 1. So losing havens increases it permanently? Should keep that in mind. And yeah, after destroying a lair/citadel, a few minutes after that it goes up by 3%, up to 21 or so, then a haven is attacked. Again this is specific to one of my campaigns.
I remember in one the campaigns that I also ended up abandoning, because it was super tough from the start, basically, 3 weeks in-game time, ODI at 6%, a haven defense with extreme difficulty popped up. Of course, with a Scylla in it, that early in the game. After that the whole area was lost, no time to get rep or resources, level up etc. So I guess it's just completely random.