Robert Phemister was in one post office directory but apparently added later and not indexed, I had to find him by turning each page. The age of 21 was if that Alexander that I found born in Dallas would have been the correct one, so another reason for thinking it was not. But there is that little factor that there wasn't nine months between the marriage and the birth...
However, in reading over my records, I realize that there may be another solution.. Robert married a wife [Hannay or Hannah] who was definitely of Ayrshire, and they definitely visited there. So perhaps the family note of "parents who were natives of Morayshire" should read "parents who were natives of Ayrshire" and I have been looking in the wrong place.
The family notes come from a family bible, but someone who has seen the page says it appears they were all written at the same time by the same hand, not appearing to be collected at the time.
Thanks all who have responded for your help.
All the good records I've found have been from Scotland's People, there are just so many people with the same names!