Praise be to Allah.
We put this question to our shaykh, ‘Abd ar-Rahmaan al-Barraak (may Allah preserve him) and he replied:
So long as the money in the fund is no longer in the possession of the donor, no zakaah is due on it. Similarly, no zakaah is due from the poor person, because he has not taken possession of it; rather it has been placed in a regular charitable fund, over which the poor person has no control. So what appears to be the case is that no zakaah is due on this money.
For more information please see the answer to question no. 125370.