The trade's crypto is always protected by the escrow. The counterparty's payment is made through whatever method both sides agree on: it can be another crypto (crypto-to-crypto trade) or an external method like a bank transfer (crypto-to-FIAT trade).
Coordinate the method and the details through the trade's chat, and only declare/confirm the payment once it actually happened. The escrow protects the crypto, not an external payment that was never made.