Whenever it comes to researching very old items like the whole Manchac/Menchaca origins, I always love to look at Google books. They have some really old stuff that has been OCR'ed and is searchable.
In this case, I was primarily interested in 19th century texts. It seems to have been referred to both ways even 120+ years ago (it's pretty logical to assume the place was named after the springs, and the road named after the place).
The results? Inconclusive, but I kind of lean towards Manchac because of the older references (particularly the 1859 list of post offices, which list Manchac, Hays, Texas)
Example searches -
https://www.google.com/search?q=manc...x:1899&tbm=bks
https://www.google.com/search?tbs=cd...+springs+texas