I just played a game with my buddy against 2 AIs and the culture behaved somewhat erratic in my opinion.

I had a volcanic planet, which i upgraded with industrial upgrades, as i had 3 shipyards there. Right next to it i had ice planet, which upgraded with social upgrades and built 5 or 6 media hubs there. It showed the culture rate to be 49 from this planet - i maxed the culture research as well.

Despite that, the allegiance on said volcanic planet kept falling down, as it was 2 jumps from enemy desert planet, which produced culture at 30 per second rate (sent scout there). I built 2 more media hubs on the volcanic planet, despite the industrial orientation. Eventually the allegiance fell down to 22 and for some reason started to raise back up. Dont really know if it was down to those 2 more media hubs or what, but it still did not make sense to me, as my ice planet seemed to generate more culture and was one jump closer...

My buddy lost some planets to the culture and claimed to have 5 culture centers there as well and still it was not enough. Either something is really bugged or the new system made culture far more powerful than it ever was, on par with military conquest i would say. In a way this was what people wanted, especially for Advent - but this was actually TEC culture i am talking about.