No, it is per turn. But it is rewarded at once to the spying civ after finishing. I haven't tested what happens if you catch the spy - do you get all the money back?
Cash is taken every turn, and it put you in the negative every turn. I had about 75% of my army taken out by multiple spies on my commercial districts in a recent emperor level game. That was quite surprising and there was nothing I could do about it.
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