The apps I listed are light client phone apps (no node is running on them), what you do is connect to one of a number of trusted public nodes or your own node.
Even with a Monero public node, the privacy you give up is not nearly as severe as connecting to a public node on Bitcoin. The only thing a malicious node could glean is your IP address (you could hide this behind Tor or VPN) and find out the the true spend in a transaction. But the reciever and amount would still remain unknown to them.
So a malicious public node could potentially know the true spender in a ring of decoys, but never *how much* was spent or *who* recieved it. Which is not very much info.
But, ideally, you would want to run your own node at home and have your phone wallet connect to it while you're away for maximum security and privacy.