Alma uses a different direction for time than we tend to use. We might see casting our minds forward as looking to the future. That is not the meaning here. In this case, it is what we would term casting our minds back to an earlier time. We don’t have an explanation for this idiomatic way of using the language, but it is clear from the context that Alma is telling them things about the past that inform them of their present.
Alma reminds his audience that God ordained priests to the priesthood. Our reference to the priests “after his holy order” would be to the Melchizedek priesthood, but the Nephites do not make that kind of distinction in their priesthood. For them, priesthood comes from God and provides the right to perform ordinances and to teach in God’s name. There is no division in the priesthood about what may be done by different priesthoods. Authority was authority, and authority from God was power from God.