It's a per turn bonus so, to take the standard ethanol corp example, each three cities gets +3 beakers/turn once they have a corp. The bonus is applied like the one from a specialist is.
I run universal suffrage, free speech, emancipation, free market and pacifism.
Well, while I understand how it can be beneficial at home even if it cost money to maintain, I still don't understand why one would want to expand corps abroad. The creation fee in a city of a neighbouring civ was around 275g (so I guess more if you send your executive farther) and given that at the time of corps the game is usually almost finished, I hardly see a point in spending shields for the executive and money for the creation of the corp for so little benefit, if any.
BTW the other civ doesn't loose the resource, it is just that he can't creates a corp using the same resource in that city, unless he spends a massive amount of cash to remove the competitor. Actually, getting foreign corps is rather beneficial if you have the financial power to sustain them. In my game, Hatshepsut spread her creative construction corp in all my cities, giving them +2

and +7

each so it was more a blessing than a curse. I was her staunchest ally and it seems AI will only spread corps in friends territory.