I don't feel that it is your entire culture per turn, otherwise we would get falling status much more often. Yet it is pretty common for it to be rising even when the person only has 2 tourism, while you generate like 50-100 total culture per turn
And that's expected to happen, because you start stockpiling Culture before you can stockpile Tourism. In the beginning it will always be "rising", independent from the actual difference.
A quick example with random numbers:
Imagine you have 1000 Culture stockpiled. You get + 50 every turn. An Enemy AI just got +2 Tourism.
(tourism/culture on Turn X)
0/1000 on Turn 1 -> 0%
2 /1050 on Turn 2 -> 0,19%
4 / 1100 on Turn 3 -> 0,36%
...
200/6000 on turn 201 -> 3,33%
...
1000/26000 on turn 501 -> 3,85%
Although you produce +50 every turn and he does only produce +2 Tourism the actual percentage rises, because there's just no tourism pooled yet. The gain slows down once the tourism-pool gets bigger and would - if the game were to go on forever and the numbers never changed (and if my math is correct) - stagnate at 4% (actually 3,99999~, but 3,99999~ is equal to 4) total influence (because 2 is 4% of 50).
Not sure if that's really how the game displays rising/falling influence, but from a purely mathematical point of view, the bigger your total culture is and the smaller the AIs tourism is, the easier it is to get the total percentage to be "rising" over a long period of time. That doesn't mean anything though, as long as you keep their tourism-gain below your culture-gain, they will never overcome your culture (with passive Tourism).