I see. Strike now does have a Bitcoin wallet (account) as well as the USD wallet (account), but that doesn't interact with lightning. There is a Send button so I can pay bitcoin on-chain, but there is no Receive / Deposit for bitcoin, as far as I can see. You can buy (and sell) BTC from this wallet (account), so at least you can self-custody your coins.
But for LN payments, you are correct -- incoming sats (via LN) will be added to the USD balance, and outgoing sats (via LN) are subtracted from the USD balance.
For internal / account-to-account (i.e., send to another Strike user), the amount is in dollars only.