Before I answer your question, I wondered why you wish to travel to Geneva to take a train to Italy, while the train to Italy will serve Geneva-Brig-Milan? There is no need to travel to Geneva, you can simply join the train to Italy in Brig. There are direct trains from Zermatt to Brig.
The Saver Day Pass is valid on any Swiss train; it allows travel at will, therefore no specific train number is indicated. On Swiss trains, there is free seating. This is why it does not come with a seat reservation.