If this is a large unit with differential protection, making the instantaneous trip highly sensitive is not really necessary. I would err on the conservative side. It's actually more problematic for transformers protected only with primary fuses, since the fuse TCC is more or less fixed, and replacement in the event of a nuisance trip is more difficult than resetting a relay. It can also be an issue for smaller tranformers protected with molded case circuit breakers. For larger transformers the instantaneous trip (primary) needs to be set above the maximum secondary fault current, and in many cases this will be higher than the inrush current unless the impedance is very high.
Gunnar - were the transformers unloaded on the secondary when energized? Just curious. Thanks for posting.