Correct, it's non custodial. When you need a larger channel to receive more sats, there's an onchain fee to splice in more liquidity. Phoenix does automatically, the user gets a warning in the UI if the fees will be large.
Discussion
I was thinking that splicing was design to avoid the on-chain fee of opening a new channel, so what's the point? Are the fee significantly lower than opening a simple taproot channel?
It's to avoid having to open multiple channels to increase liquidity. It's an onchain tx so AFAIK no difference in cost to a std onchain tx.