As discussed earlier, Alma's baptism became the sign of assembling into a church. It is this context in which we need to see the Limhite's desire. They have been through tribulations occasioned by the death of Abinadi, and have seen Alma come through that experience with a renewed covenant with God, and at least the obvious blessing of not being a tributary to the Lamanites.
It makes the most sense for Limhi and his people to desire to do what Alma has done, but become a "church." There is no clear indication of a "church" in Zarahemla at this point in time. There will be churches there, but only after Alma's arrival, and probably at his instigation.
It is quite possible that Ammon is balking not at the right of baptism, but at the greater implication of the formation of a church, an authority that he would not presume, even assuming the authority to baptize. Ammon is probably deferring because he is being asked to perform a rite with a context and meaning with which he is unfamiliar, and therefore would prefer to wait until he gets an indication from Zarahemla as to how they should proceed.