Actually, your crypto asset is on the blockchain, and you manage the asset with only proof of your ownership of these assets---the private key. SafePal App or SafePal server doesn’t store or access your private key or crypto assets.
S1 hardware wallet is a tool helping to keep your private key safe and protect your asset from malicious hackers.
The SafePal App is responsible for all interactions with the internet and blockchain.
Balance won't be automatically synchronized to the S1 hardware wallet since the device is 100% offline. Especially when someone sends you money, thus meaning the balance on the S1 hardware wallet won't be an accurate number. It's not until it signs a 'sending out' transfer then it 'knows' the existence of this newly added token. After you pair the hardware wallet with SafePal App you only need to check the balance on the SafePal App.
So to answer your question, you don't have to transfer your asset from SafePal App to the SafePal hardware device, because both of them don't store your asset, they just protect your private key and seed phrase.
Hope this could help!