Welcome to ____. Exit right enable. Taxi to the ramp on this frequency.

On a few occasions, when ground was offline, I've received this instruction from tower/radar/center controllers after landing.

I mostly understand how the actual runway-taxiway-ramp procedure works, but I'm not sure about the intent of remaining on that frequency.

Does this mean I'm expected to turn off, hold short, then call again to the controller for taxi a few seconds later? Or does it just mean taxiing at my discretion while still monitoring the same frequency?