I can tell you how it works for us but you may want to double-check with your agent/management company if this is the same for them.
Although the Management Company (of which you are a member) are the policyholders, generally speaking the individual submitting the claim is responsible for paying the excess. This is standard business practice.
The only time when this may not be the case is if it can be proved that the damage was caused by some malfunction in the common areas. In which case it could be argued that the Management Company are at fault and should pay the excess. They would not necessarily be legally obliged to do this but they may decide to do so, to be fair and reasonable.
However if, for example, the apartment above you flooded and caused damage to your property, as you are the one making the claim you will be responsible for the excess. This seems very unfair (and is!) but unless you can persuade your neighbour to contribute to the excess out of decency, you will be liable to pay the excess personally.