What's going on with this FirstPassageTimeDistribution performance quirk?

Question

Observe:

SeedRandom[1234];
dmp = DiscreteMarkovProcess[1, 
   Append[Normalize[#, Total] & /@ RandomInteger[{0, 100}, {29, 30}], 
    UnitVector[30, 30]]];

ClearSystemCache[];
Mean[FirstPassageTimeDistribution[dmp, {30}]] // AbsoluteTiming

ClearSystemCache[];
Mean[FirstPassageTimeDistribution[dmp, 30]] // AbsoluteTiming

Same result (as it should be) but on my machine (10.3 Win), the latter is well over an order of magnitude slower.

Genuinely puzzled by this behavior, wondering if there's some internal optimization used when conditioning on reaching the desired state...