Connect wallet, then pump
Two signatures, two boundaries. Neither gives calld custody or spending permission.
Wallet ownership
Your wallet proves account ownership with a message signature. It does not give calld custody or spending permission. On mobile, open the page in Phantom and complete the same signature there.
Linking pump
Linking pump is a separate message signature. It authorizes access to your pump account, so keep that boundary distinct from wallet ownership. Disconnect pump at any time to stop that access.