Chaps,
It is mainly a TRANSIENT phenomena. If it wasn't, the aircraft would continue to yaw during a continuous aileron roll until it was flying sideways!
To accelerate the aircraft in roll does require a difference in the lift that is produced by each wing and hence the difference in drag experienced by the wings, causing the adverse yaw to begin.
However, the aircraft also has stability by virtue of it's wing dihedral. To oppose this and hold the aircraft into the turn, some aileron will need to be held, prolonging the phenomena.
Any small increase in lift causes a large increase in drag (increase in drag = increase in lift squared).