A follow up. Looking at Table 450.3(B) with primary protection at 125% and secondary protection not required, this would mean the OCPD upstream would never trip unless the primary load exceed 125% of the transformer's FLA?? Transferring that onto the secondary, does that mean a the transformer would never trip with 125% of it's secondary FLA? So a 225 kVA transformer could run 625A x 125% = 781 without damage or just without tripping?
It's only qualifying topologies, where the primary OCPD can be considered to protect the secondary conductors. To qualify, it requires overcurrents to line-up across each winding pair, and not get redistributed. Anything involving a centertap, a wye system on one side, or both, does not qualify. If you have a centertap, but don't connect anything to it inside the transformer, it counts as if it wasn't there in the first place.
As an example of why, consider a 480V to 120/240V 1-phase transformer, with a 50A breaker on the primary. This would imply a 100A secondary circuit if it were 480V to 240V straight instead. With the centertap, consider drawing 150A on Leg 1, and 10A on Leg 2. This will show up as 40A on the primary, which the primary breaker ignores. The overload on Leg 1 is in its blindspot, which is why a breaker on the 120/240V side is required, to meet 240.21(C).
In your situation, the fact that it could run at the full 225 KVA doesn't govern what you need to connect for a secondary circuit. You are only required to size your secondary circuit, for the calculated load that will be installed at the time you finish your job, with the continuous load safety factor (if applicable). If you only use 170 kVA continuous (hypothetical number) of the 225kVA, that's 472A yielding a 600A OCPD, and it would be OK to use a 600A OCPD and circuit. The fact that the transformer has more capacity, doesn't require it to be higher.
800A would give you the full capacity whether continuous or non-continuous, while the 625A figure you mentioned would likely round up to 700A in practice, if you wanted to use the 225A as non-continuous. It's best to stick to standard fuse ratings where you can, to facilitate replacements in the future.