The rule you are looking for is 4-2-2 and the definition of forward progress in 2-15-1, but the answer you are looking for is in the interpretation of the rules. In my area, we operate on the idea of giving the runner what he earns. No more, no less. A runner who steps out of bounds gets the out of bounds spot and the clock stops. A runner who is driven out of bounds leaves the covering official with a decision to make: where did the runner's progress get stopped? If the progress was stopped in bounds--even if the runner was still on his feet--the ball is dead there, meaning that the live ball didn't go out of bounds. By the time the ball was out of bounds, it was dead, regardless of whether the whistle sounded.
It is sometimes tough to determine if the runner was moving forward or was driven forward out of bounds. I won't lie, coach: when there is room to do so, most of us rule that he was stopped in bounds to keep the game moving. If he wanted to stop the clock, he should have gotten out of bounds on his own. (Similar to how we start a new series on a tick mark if at all possible, even if it means taking or giving a fraction of a yard to make managing the game a little easier.)
P.S. Welcome to our little corner of the internet. It's always nice to see coaches looking to learn and engage in useful ways!!
Edits to correct typos/punctuation.