For a planet to be considered under the effect of your culture, you have to overpower enemy culture.  Your culture must not only dominate the entire phase line leading to the planet, it must completely overwhelm the planet and continue to move across phase lines in the other directions.  Any enemy planet with enough culture to give you a military bonus is losing allegiance.  In general, this makes it very difficult to fight in enemy gravity wells with your own cultural advantage.

In general, culture is something more defensive in nature, and difficult to use offensively.

You can actually see this effect in action too.  Cultural influences and effects operate on a sliding scale, instead of being an on-off affair.  If cultures meet at a planet, it is considered to be culture neutral(though the alliegance will increase for the owner of the planet).  If one culture begins to overtake the opposing phase lane, any benefits given by that shift slowly start to take effect in small increments. 

The easiest way to see this is with a Vasari starbase, especially if the pulse gun damage upgrades have been researched.  You'll see the attack values creep up digit by digit.  The displays truncate the decimals, but the values are constantly shifting as the culture updates within the game.

In any case, the full cultural bonus is only applicable to a gravity well whose connected phase lanes are ENTIRELY filled with friendly culture. Even filling one lane with opposing culture will reduce the bonus granted.