Fix what? Your culture changes during the game. Just because you picked one culture at start doesn't mean you will stay that culture, or even become that culture.
For example lets say you picked the Greeks as your civ. They are European base so different European cultures can develop if you have the right resource nearby. Then you take over say a Japanese city. Now you empire has an Asian influence to it was well as European. As a result Asian cultures can develop in your empire too.
The more regional cultures you assimilate, the more cultures you can unlock. If you do not like this then turn assimilation off and you will only get the cultures within your region.
What that would likely be a matter of is the cultural output of cities is vastly improved with a lot of new buildings, thus, when you take a city, you're plugging out a lot more culture than the initial formulas for that would've expected. I guess that doesn't bother me much but it might be interesting to take a look at HOW thee percentages are actually calculated to see if some balance factors are off and how we can adjust the formulas to reflect that fact.
the fact that is unbalanced is sure . after 5 turn the city turns to your nationality is not balance
Are you referring to cities near your borders? I know that often when I strike at a city, my culture is usually surrounding it heavily already, so that means its influence has already been working on the people of the city long before it is conquered.
I just remembered... the game option... influence driven war. Turn it off when you start your next game and see what happens. You're probably half earning the city's populace over as you take the city.
this is a measure of culture present in the city tile if I remember correctly, are there any mechanics that remove enemy culture on capture?