Unless I've played it wrong a whole lot of times (entirely likely since the game was taught to me and I haven't read the rules, and neither has Mister Bananas), the start player each round is the owner of the sack (who is the person who won the auction in the previous round).
You are correct. The rules say
When all the cards are turned over, there is now just one player who has not passed. He pays his bid to the bank and he gets contents of the sack: all cards (with positive and negative values) and puts them face down in his play area. The player places his won cards separately from those in his hand. He also takes the start player marker.