So it looks like any control, not just the specific hex being attacked. So, for round 1:

Eldar: +/- 1 to reserve rolls against Chaos, no bonus against Imperials
Chaos: no bonuses, because other factions have more command bastions
Imperials: +/- 1 to reserve rolls and +1 to rolls for objective placement/table sides against Chaos, +1 to rolls for objective placement/table sides against Eldar

I'm counting 1 vs 0 as "More" although I could see it be triple.

That look right to everyone?