What exactly is the mechanics of gaining/losing money for protector/protectorat

[Bactron]

I have never been subjected to being a protectorat of other faction.

But I have subjected some factions couple of times into my protectorates.

How exactly does it work with relation to faction treasury. I think that protectorates gaves all the money they have every turn to their protector. Am I right?

And if so, could it be modified so for example: protectorates would give only half the money they make for turn to their protectorates? It would actually make it reasonable to accept position of protectorate even for human player in some situation. Because you would gain strong alliance (with ai faction that probably kicked your ass badly) and also you would still have at least some money to handle your own factions needs (building cities, army upkeep, hiring new units etc.)