Game progression plays and unlocks them.

Cutscene	How to unlock
Abducted Friends	Complete Green Hill (Classic).
Are We in the Past?	Complete any Act of Chemical Plant.
Eggman Abducted	Complete Egg Dragoon.
Eggman Abducted	Complete Death Egg Robot.
Ending	Complete Time Eater.
Restoring the World	Complete Seaside Hill.
The Dark Monster and the Chaos Emerald	Complete Perfect Chaos.
The Final Battle	Select Time Eater.
Through the Glass	Select Death Egg Robot.
Trapped!	Complete the game.
Two of Me	Complete the first Area.
Two Sonics	Complete Green Hill (Modern).
You Got a Chaos Emerald!	Complete Planet Wisp.