Commercial Fixed Wing
Air Traffic Control Fully Certified
Communication Breakdown; Distraction
ATC Issue All Types; Deviation / Discrepancy - Procedural Published Material / Policy
General None Reported / Taken
Company Policy; Environment - Non Weather Related; Human Factors; Procedure
I was combined everything for the cleansing of the cab.  Aircraft X landed Runway XX Left; and while rolling out I checked for their gate.  They were going to the Ramp as they must have been an International arrival.  I issued them keep their speed up to Tango; traffic two miles in trail; then taxi via Bravo to the ramp and to contact Ramp prior to Bravo [X].  They read it back. Once they exited; I resumed my end of shift clean-up before the first mid shift person showed up in about 7 minutes.  There were no other aircraft to work.  I gave that next arrival the same instructions (to the Ramp via Bravo) and left out the Ramp contact as they are regular users of that Ramp Control.As I continued to clean; the line rang from Ramp Tower.  When I answered they asked me to have Aircraft X call them as the flight was taxiing in without communicating with them.  I hung up the line and tried Aircraft X.  The second call they answered and I told them they should have called Ramp Control at Bravo [X].  The pilot communicating said 'We are working on it.'  I have thoroughly provided anyone going into the Ramp; while the other Ramp closed until traffic picks back up; with the exception of Air Carrier X and Air Carrier Y aircraft the exact communication changeover stated in the previous narrative.  I really do not know what else I can recommend other than them calling as described and read back.
Tower Controller working combined positions reported an aircraft did not call Ramp Tower as expected.