In a conventional crease slide package the first slide comes from the crease. This is effective because typically if a dodger beats his man he will be running toward the goal and therefore right at the crease defender therefore he is generally closest and at a good angle to approach the dodger.
However a crease slide becomes weak when you face a team with a strong alley dodger or with an offense that uses sweeps across the top. In both cases the dodger is not running towards the crease.
So now who is closer, and who has the best angle to turn away the dodger? Many teams will want to introduce the adjacent slide in these situations.
Dodging down the alley