Follow me on this theory... I think popping tiles is a bit more "organic" than systematic. At least the engine tries to replicate organic expansion.
All tiles that are adjacent to owned tiles are continuously getting a portion of culture, with the two or three "best" prospects getting a higher percentage of culture. Maybe it's 30-15-10 then split the remaining 45 equally. The numbers are just used for explanation. Either way, all tiles are getting SOMETHING each turn.
So, in turn 1, Tile 1 gets 30, Tile 2 gets 15, Tile 3 gets 10, the other 9 get 5 points each.
Turn 2, Tile 1 is at 60, Tile 2 is at 30, Tile 3 is at 20, the other 9 are at 10 points each.
Turn 3, Tile 1 is at 90, Tile 2 is at 45, Tile 3 is at 30, the other 9 are at 15 points each.
Turn 4, Tile 1 pops at 120, Tile 2 is at 60, Tile 3 is at 40, the other 9 are at 20 points each.
Add 3 more tiles to the mix. One of which is a great tile that replaces Tile 1. Meanwhile, Tile 2 and Tile 3 already have points accumulated, but the new Tile 1 still gets the biggest percentage.
The next turn, Tile 1 (new) is at 30, Tile 2 is at 75, Tile 3 is at 50, the other 11 tiles are at 24 points each.
And so on...
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Again, the numbers are fictitious and exaggerated to explain the theory. But to me, it seems like all tiles get a steady flow of culture, which is why some tiles that you would think would pop do not. If they are in that lower tier the entire time, they are getting the least amount of points per turn.
This is an effort for Civ to replicate organic expansion, as people are going to "tend" to flock to where the "jobs" are (i.e. better tiles), but they will still expand outwards from all tiles, even if the jobs suck.