Generically, the transformer impedances are related to short circuit current levels, voltage drops, transformer cost, transformer efficiency, harmonics, industry impedance standards, network stability, etc. One simple answer may or may not cover all important aspects of your transformer application.

Are you sure that the impedances stated are for the correct voltages?  If you calculate the actual impedance values per phase using the formula Z= (%Z/100)*(KV^2)/(MVA), you get the following values -
11.5 KV, 12.5%:  Z = 0.125*132.25/250 = 0.066125 Ohm
15 KV, 20%:      Z = 0.20*225/250 = 0.180 Ohm
These are very disparate values, which leads me to think that the values are in fact reversed, as follows -
11.5 KV, 20%:  Z= 0.20*132.5/250 = 0.106 Ohm
15 KV, 12.5%:  Z= 0.125*225/250 = 0.1125 Ohm
These results appear more reasonable, as the 15 KV connection will have a somewhat higher Ohmic impedance than the 11.5 KV connection.
Recall the definition of percent impedance - it is the percentage of rated 3-phase voltage that must be applied to a winding of the transformer which will circulate rated current in the winding, with the other winding of the transformer short circuited.
As jbartos states, the impedance will influence the short circuit level - this could be a concern when the transformer is used to connect the 110 MW set, as the 11.5 KV bus duct (assumed that this is the connection method) may be braced for a lower fault level.  Assuming an infinite bus on the HV side, the transformer will deliver a maximum of (250/0.2)= 1250 MVA RMS symmetrical into a 3-phase short circuit on the LV side (this assumes that my analysis above is correct for the 20% impedance applying to the 11.5 KV connection).
This and the other concerns for generator operation with this transformer need to be addressed by a series of system studies to confirm the application.

Suggestion to the latest posting: The generator with an approximate generator subtransient reactance Xd"=0.1 p.u. will deliver 250MVA/0.1=2500 short circuit MVA RMS. Therefore, the lower voltage transformer side power distribution must be rated for that short circuit MVA. The higher voltage transformer side will include the transformer impedance so that 250MVA/(0.1+0.2)=833 short circuit MVA, which could be used as a base if the opposite side of power distribution network does not deliver the higher short circuit MVA.