Sizing the pri. conductor and the related OCP device based upon the actual load is often done. You have more than adequately protected the transformer and have sized the pri. OCPD to protect the cable.
But, you omitted stating the primary and secondary voltage of the transformer that I'll take a guess at. I'll assume it's a 480v pri. and a 208y/120 secondary transformer. The pri. FLA will be 90a. Often times the installer in limited to no larger than a 100a OCPD by the panelboard itself. If one considers NEC art 450.3 and table 450-3(B) you are allowed 125% to as much as 250% depending upon the installation, that's 112.5a-225a or a 125a and up to a 225a OCPD dependent upon the installation as I understand the NEC.
the inrush current of a 150degC transformer may be anticipated at around 10x the rated FLA which in this case is 90x10=900a. The question then becomes will the breaker trip instantaneously when the is energized. (Transformers with high KVAs will generally be less while those with lower KVAs can range up to over 20x.)The common breaker's instantaneous trip is 10x its rating +-20%. It could be a bit tenuous if the breaker trips or not. To add insult to injury the inrush increased with 115degC transformers and K4 transformers and even more with 80degC and K13 transformers.
It is of my opinion that it may possibly boil down to if you feel lucky or not.
Again, my inrush figures are based upon what may be expected as ther has been not reason to run test to establish inrush values on the different combinations of KVAs, temperature rises, and K-factors. It's not necessarily a "black and white" issue but a means to determining what may be causing nuisance tripping and where a problem my possibly be created when sizing the pri. OCPD.