When the button is turned on (bright green), the behaviour is most like a tape delay, in that the play heads slide along the tape to their new positions. This will inevitably produce some odd sounds if the tape is not empty.
With the button off, the play heads move instantly, which is not how a physical tape delay works, but allows you to change the delay time without the unusual sounds.
In fact, it is a little more complex than just described - the play heads don't move instantly. Rather, new play heads are created at the new positions and the sound from these is faded in as the sounds from the old heads are faded out. The duration of this crossfade is controlled by the 'Inertia Fade' knob (set in milliseconds).