Ya, you have to have your Zeus embedded LND up and running. Darth's guide is a great resource for how to get started with Zeus embedded LND, and to get your zaplocker set up (the zeuspay ln address) - https://darthcoin.substack.com/p/getting-started-zeus-mobile

Once you are all set up and have a channel with liquidity, it's a matter of configuring your stacker news wallet with the ln address from your zaplocker as outlined in my article. Yes, the sats that flow into your stacker news ln address will be there until you either open your zeus wallet and manually redeem sats sent to it from the stacker news wallet, or you have your zeus wallet on persistent mode and turn on auto redemption and it should do it seemlessly at that point as long as zeus is on in the background.