My understanding of flavours is very incomplete, but flavour values on buildings, units, policies, techs, etc are at the very end of the AI's decision making process. "Strategies" play a far more important role in what the AI does.
A civ has a leader. The leader has base flavours (see table <Leader_Flavors>). The flavours help the leader choose the victory condition it's going for. The VC then helps determine the associated Grand Strategy (see CIV5AIGrandStrategies.xml), which adjusts the leader's flavours.
During the game, the AI adopts various Military and Economic Strategies (see CIV5AIMilitaryStrategies.xml and CIV5AIEconomicStrategies.xml) the rules for adopting these are in CvMilitaryAI.cpp and CvEconomicAI.cpp (yep, you're going to have to dig into the C++ code to fully understand this). The military and economic strategies currently adopted set base flavour values, but we're not quite done yet.
Each city also adopts various City Strategies (see CIV5AICityStrategies.xml and CvCityStrategyAI.cpp) as the game progresses, for example, after it's just founded it will want to grow, but once it's reached a certain size it will start to specialise depending on the AI's VC, the current Economic and Military Strategies adopted and partly its surroundings (inland cities will not specialise in naval production!) The cities base flavour values are then the Leader's base flavour values adjusted for the specific City Strategies currently active for the specific city.
When a city needs to build something, it pretty much already knows what it's got to build from the base flavours - the real driver for what is actually built are the currently active strategies. Building/unit flavour values only really affect decisions like "I need to build a culture building, which of the two available shall I build" or in the early game (when very few strategies are adopted) "which of these three similar cost buildings should I pick based on my leader preferences (flavours)"
Policy and tech flavours are similar. The currently adopted grand, military and economic strategies are pretty much driving the AI down a path, and the policy/tech flavours just influence what to do at junctions.
So if you have the AI players all adopting the same policies, it's either because they've all adopted the same VC and hence the same Grand Strategy, or your modifications have forced the AI to adopt similar Economic and/or Military strategies - possibly because you've stopped the AI expanding by settling and it's stuck in expansion mode - either by founding new cities (economic) or by conquest (military).
And the part of your OP we don't understand is " they complete 4 branches at max (while culture is enough to complete 20)" which implies the AI is not spending all of its culture.