Hi Wall_E.
Matt is correct, the only way to get the SAG jackpot (and it can be a jackpot) is if you sing on a commercial that is produced by a SAG signatory ad agency. You do not need to be a member for your first one, although afterwards, you become a Must-Join. Unfortunately, in order to go down on a SAG contract, you need to be eligible to work in the United States, with a valid Social Security number.
As for getting royalties each time a commercial airs, that is correct, in the United States. Unfortunately, in Italy, SIAE does not pay royalties on commercials. If you had commercials airing in the US, you should be receiving royalties generated by your US subpublisher/publisher.
Eric