Protectorates do not screw your income. It is exaclty the way it is. The finance tab shows you how much you got THE CURRENT TURN. And the projected profit will mean how much you will have next turn if nothing messes with it. In this case. AI gives you 10000 in turn 1 which is showed on your finance, You press end turn, AI goes into the red, AI does not give you tribute the next turn so you dont get the money. Its basically a misinterpretation, Like when you recruit 1 unit of cavalry which costs 1000, and has a upkeep of 400, the 400 upkeep deduction will not be counted in your projected income for the next turn.