Every turn each city adds its culture to every tile in its cultural radius - with a bonus of 20 for each time its cultural level has increased after reaching the tile.
Example: IF a city has expanded twice and produces 2 culture per turn it will add 2 culture to the 16 tiles outside its BFC but in its cultural radius, it will add 22 culture to the outer 12 tiles of its BFC, and 42 culture to the 9 central tiles.
A city adds to every tile in its cultural radius regardless of other factors, A tile is added to be every city whose cultural radius it is within.
A tile is controlled by the empire with the largest amount of culture in the tile that has the tile within one of its cities' cultural radii. Except that a vassal "gives" control to its overlord if it is in the BFC of one of the overlord's cities.
A tile with a city doesn't change with culture, however this puts it under "cultural pressure" which brings a risk of revolt and can cause the city to change nationality.
The percentage shown on the map doesn't change much because you are usually talking about small changes - say 20 - in a large accumulation - often 1,000's or 10,000's.