On a Constellation so far, most, if not all, I have seen has metallic "OMEGA" wording on the dial instead of printed. Is my assumption correct?

Now on a Seamaster, I have seen both printed and metallic OMEGA on the dial. Myself, i have a Seamaster chronometer cal. 564 with metallic Omega. How do we know which the original dial should have?

 

You know by instinct, careful observation with a high power loupe, and review of contemporary models of the same era.

There is no hard and fast rule (with the exception of those documented, e.g.: for Speedmasters. Even then there are transitionals).