There isn't much known about either the Changing or The Banishment, as the events in both the book and movie happen near the end of the Maze events. Every rule was created by the Gladers long before Thomas shows up, so there is much unknown. What we can see though, is that the Changing doesn't effect everyone the same. Only four people are seen going through it, Ben, Alby, Thomas and Gally. We only see Ben being vanished, and he's pretty manic when it happens. Alby and Thomas both get stung, take the Grief Serum, and then are okay. Gally almost acts like Ben did.
Keep in mind, in the books, the Grief Serum already exists, so its always administered if the stung person is found in time. And Book Gally went through the Changing before Thomas even arrives.
This leads to the main question, why would Minho attempt to save Alby when Ben was Banished after being stung? Aside from having to match the book version where this is a major event, the Banishment of Ben seems to happen due to a separate reason. In the book, Minho's main reasoning is that there is a cure for being stung, so leaving Alby, their leader, in the Maze would be the same as killing him. There's a chance to save him. Ben, instead, was banished not because he was stung, but because he attempted to kill Thomas. Hurting another Glader is one of the worst things you can do, and the Rules required he be removed. I believe it had to do with Ben not being given the Serum in time, and that leaves him crazy and dangerous. The Gladers had no choice.
In the Movie Alby, unlike Ben, when stung, spends a week or so sick. If we consider that not everybody stung reacts the same as Ben, then the movie answer would simply be the same as the book. Ben was banished because he became a dangerous lunatic after the Changing, not because he was stung. While one happened because of the other, the end result is the same, only the Dangerous ones get Banished. So Minho, knowing this, would attempt to save Alby, because it was not guaranteed that he would become dangerous.