Abish is already a believer. She is a believer before Ammon arrives, having become converted to the Lord through her father. This statement is given in the text to explain why she is able to resist the outflow of the spirit. It is not that she does not believe, but that her prior belief allows her to feel and understand the spirit without being overcome by the newness of it. Certainly, the conditions required that there be someone to interpret this mass physical effect of the spirit.
Her conversion itself, however, is an interesting puzzle. Abish is declared to be Lamanite, and as a Lamanite, she should have followed the beliefs of her people. Doubtless her father, prior to the life-changing vision, was also one who followed the traditions of the father. As Lamanites in a city that has no clear connections to Nephite cities, how does this father understand his vision, and his daughter believe sufficiently to play her role in this event?
It is entirely possible, of course, that the vision of her father had no particular precedent that a response from God to the desires of a sincere man. He could easily have seen, and believed. It is also possible that there was some understanding of Nephite religion present in the Lamanite nation. While they did not believe, it is quite possible that they understood their beliefs as standing in contrast to those of the Nephites. That is, while they did not believe, they at least understood the general outlines of what the Nephites believed. Since we know that the Nephites were able to generally categorize Lamanite beliefs, this is completely probable. As a final possibility, we must remember that this is only one generation removed from the departure of Limhi from Lamanite lands, and that generation would be the generation of the father. It is therefore also possible that the father had some contact with the Limhites at Nephi-Lehi, or perhaps with Alma’s people, and that his vision came as a confirmation to questions asked about the God of these people.
Textual: Abish is one of the very few named women in the Book of Mormon. That her name is present here is even more remarkable because she was a servant, and the records of the world typically record the names of royalty, but not the names of servants. The presence of her name, and the details of this little aside, suggest that Abish was more important in the original record than we see her in Mormon’s account. While the description of her conversion provides an explanation of why she did not fall down, nevertheless, it would not be anything that would require that she be recorded by name when other women, such as the queen, are not named. This contrast between the named servant and the unnamed Abish hint at a much more important role for Abish in the establishment of the gospel through Ammon than we have in our records.