This is an iOS problem rather than a Scrivener one, but is there a solution: iOS has been set to auto-capitalise after a full stop/exclamation mark/question mark followed by a quote, so you get something like this:
“What’s that?” He said.
Apart from disabling auto-capitalisation in the Keyboard prefs, is there any way to stop it doing this?
Not that I’ve noticed. 
Others who find this a problem might like to add feedback under iPad on the Apple feedback and support page - apple.com/feedback/ Maybe then they’ll change the coding.
Meanwhile, the most sensible thing seems to be to buy a Bluetooth keyboard case, switch off predictive text and automatic capitalisation and type in your words on the external keyboard.