In a co-op game, what determines each player’s hourly city income

Hourly income is tracked separately for each character based on what that character has accomplished; it's the same as if you were in a single-player game.

If you have completed an activity that gives hourly income, gained territory that gives hourly income, or purchased buildings/stores that give hourly income then you will receive that income regardless of whether your partner has done it. If your partner has completed/purchased something and gains hourly income from it, but you haven't completed/purchased it, you will not receive income for it.

Note that buildings, drug/cash stashes, sex toys, activities, etc. are all separately tracked by each client; if A has bought a given building and B has not, in a co-op game A will see the building as purchased while B will not, and B can still go purchase it. Likewise if A & B go complete an activity that B has done before but A has not, B will get the rewards for repeating it while A will get the rewards for doing it the first time.

There is one exception to this: strongholds. Only the host of a co-op game can upgrade strongholds; as with other income-boosters, doing so only benefits the host and not the other player. The other player will need to host occasionally, or load their character in single-player, in order to upgrade acquired strongholds.