Yeah. Its not really turning it off. Its just filling the SSID field in the beacon with nulls.

Your laptop/phone has to actively probe to work out what these (not so) "hidden" networks actually are. It'd be asking if that hidden network is actually <blah> SSID at which point the AP will respond and say yes or just ignore it if it isn't.

If somebody has something which can see these raw WiFi frames then they'll be able to tell what SSIDs you've got configured on your device.

Is this second network the only network configured in your iPhone?