Not addressing the idle speed increase here, but having seen the video, I would have to say the alternator does not appear to be acting normally. That is, when the volt reading is low, and the engine speed increases, the voltage does not increase as quickly as one might expect. First thing I would check at this point are the battery cables for corrosion at both ends, and the connections to the alternator to make sure everything is clean and tight. Corrosion often occurs under the insulation at the cable ends - the insulation needs to be peeled back to make sure that is not the problem. If those are all good, pull the alternator off and take it to a reputable shop for testing, and load test the battery to assess its condition.