What causes unequal phase-to-neutral voltages in three-phase distribution systems?
Each apartment is connected to one phase, different apartments are connected to different phases with interleaving so that phases are hopefully loaded equally.


Yes.


  He calls a serviceman and the serviceman claims the substation transformer feeds such voltages and the only thing he can do is to disconnect the tenant from his phase and connect him to the phase with 215 volts.


Yes.


  Is it unequal load on different phases or anything else? Also has the serviceman done the right thing or did he just put extra load on the higher voltage phase and induce risk of distribution failure?


Serviceman did the right thing.*

I think you've answered most of your own question!

The substation is presumably supposed to have some kind of voltage regulator (after all, the transformer has a nonzero output impedance, so voltages sag with load). I assume it's theoretically possible that this could be done on a per-phase basis, but my guess is that they only do it as a 3-phase set, in which case the imbalance is caused by unequal loading.

*caveat: I suppose technically someone should measure the currents out of the transformer, and make sure that the imbalance in currents matches the sag in the voltages. If the currents are about the same but the voltages are not, then it could be a higher-than-normal impedance somewhere in the distribution network.