Yes, Zeus allows you to have your lightning ⚡ address in self custody. You hold the keys and the property of the lightning channel. When you get zapped Zeus notifies you and you log on to claim those sats. Zeus it's the intermediary of the payment but it cannot steal those sats. If you don't claim them in 24 hours the payment with get rejected.

On the other hand alby is custodial, you don't have the keys or the property of the lightning address. You can get rugged. 

 I'm curious what would be the fee you paid for receiving those 1k sats with your ln address  

 Not to split hair but you can point your alby to your node as well... just saying... to each his own.