There is a backgammon rule on an illegal play or move. It states that before the other player rolls the dice, that player may request the one who executed the illegal play to correct it. If you analyze this rule you'll see that there is one prerequisite and one course of action. The prerequisite is that it's implemented before the other player rolls the dice (takes a turn). And the course of action is that the other player can either let the illegal play slide or ask the perpetrator to make it right.
The reason behind the prerequisite contained in the rule on an illegal play is that when the other player starts a turn (by rolling the dice or offering the cube), the previous play is considered final. It means that whatever checker play was previously executed, the game will go on and there's going back. The rules are pretty clear on this to preserve the game's continuance. So, if the illegal move is left unnoticed until after the other player has started, correcting it is no longer permitted.
If one pair of dice is used, questions on an illegal move hardly come up. A player's turn starts when the dice is rolled (or the cube is offered). And that's as clear-cut as it gets.
But when each player uses their own pair of dice, that's when issues arise. That's why the point of when a player's turn begins and ends is taken into account. So if each player has their own pair of dice, a player's turn starts from when the dice is rolled (or when the cube is offered) up to when the dice is picked up.
So before you complete your turn by picking up your dice you should see if you've made a mistake in playing the roll. When you do notice an error, you must fix it before you conclude your turn.
The backgammon rule on an illegal play makes it absolute that when you conclude your turn, your opponent will have the prerogative to let your illegal move stay or not. If your opponent asks you to correct it, you are obligated to do so. You must restore your illegally moved checkers to their previous positions and make a legal play that concurs with your roll. But if your opponent doesn't make this request and commences a turn, that previous illegal play is deemed final and the game will go on.