The prohibition on electors voting for two candidates from their own state seems a tad antiquated in view of the mobility of the population nowadays. While he represented Georgia in the House of Representatives, Newt was born and raised in Pennsylvania and currently resides in Virginia. So, there would be no Constitutional obstacle to electors from Georgia voting for a ticket of Cain and Gingrich.
Yes my understanding of the rule is that they go by your residence at the time of the election.