Have a look at this

The etiquette here is to post pictures, not links. That said, the Speedmaster 4.5 case back did say 'seamaster' on it (try for instance an image search for '176.0012 case back') and therefore seems correct.

It seems to be that Omega's use of 'Seamaster' sometimes paralleled Rolex's use of 'Oyster': that is referring to the water resistance of the case rather than the model name. I'd welcome more experienced members' perspective on that.

The Seamaster back on a Speedy 4.5 is correct. It does seem odd, given that earlier Mark series watches had a Speedmaster caseback, but the seller is correct - Speedmaster was originally a diffusion line of the original Seamaster. There was a thread on here a few weeks ago about earlier Mk series Speedmasters having Seamaster casebacks installed as service items by Omega, so although slightly confusing, there is nothing intrinsically wrong here.