I think the "first Vulcan in Starfleet" thing may have had to do with how the show initially evolved from the start before the Star Trek universe developed into what we know now. In the early episodes of TOS the Enterprise is specifically referred to as an "Earth ship", I think the implication was that the entire crew is supposed to consist of humans, with Spock being the exception, and possibly the first alien to join that organization. This is why there's that certain attitude from McCoy and a few others over Spock being such an outsider. That's all disputed by the end of the first season once the Federation of Planets was established. Funnily despite that, Spock still continued to be the only on-screen alien in Starfleet and the characters still treated him that way. The only other Starfleet vessel we hear about with aliens is the all Vulcan crew of the Intrepid, which we never see on screen.
It wouldn't be until TAS that we'd see any other alien Starfleet officer outside of Spock.