Amtrak will add in an extra charge for the thruway motorcoach connection from Idaho to the train station in Salt Lake City, but it is usually a very small fee. You also get the added convenience of knowing you will have a guaranteed connection to and from the train at Salt Lake City. If either the train or bus is running late, one will not leave before allowing passengers to make their connection.
If you were to book this trip you would need to order your tickets in advance by mail since you do not have a local Amtrak station in Idaho to pick them up/buy them at. Amtrak will mail the tickets to you and you will receive two Amtrak tickets. One will be for the thruway motorcoach from Idaho to Salt Lake City and the other will be for the train between Salt Lake City and Emeryville.
Hope this answers your question. Let us know if not. B)