If I have a 225kVA 4.16kv/480V xfmr in my model and I run arc-flash using ETAP.

Is it possible that the high side gets a lower HRC than the secondary side?

Let's say there is a 50E fuse on the primary side.

The results come back as Cat 0 for the primary side and Cat 1 on the secondary side.

I am hesistant to put a Cat 0 stick on the primary side. Is there something wrong with my calculations or is this normal? I have seen this in a few other studies as well.

Yes. Arc flash is current Dependant, and you have much less on the primary side.

And probably faster clearing.

I just found that to be kind of strange to have a low primary side but a really high secondary side when I am dealing with transformers in ETAP

Normal to see that. A fault on the secondary side before the OCPD will rely on the primary fuses to clear the fault, but they will see much lower current levels on the other side of the transformer and have a long clearing time.

Wouldn't the current levels be higher?

Current level is inversely proportional to voltage level.

Most people are surprised that the secondary AFIE is so high compared to the primary. This is the reason that service entrance locations are usually aove 40 cal/cm². And why the 'task table' should not be used for these locations.