What specific demo did you try?
I tried the "Sign in" form, and it works just fine for
me. I get the popup with username, password, and "Sign in"
button, and it does not bring up the keyboard.
If I tap in an input, then I get the virtual keyboard.
Are you using a third-party keyboard app? They are ALL flakey.
What version of iOS? Earlier 8.xs were very flakey.
I don't know of a JQM demo page that shows a textarea in a
popup. Can you provide a link?
I would not expect text input in a popup to work well on iOS,
though. The virtual keyboard is way intrusive in the way it tries to
take control of the WebView. There is nothing you can do to control
it. It actually scrolls the WebView inside of a native scroll window.
I work-around this in native apps that use a WebView. I use native
code to defeat that scrolling, and then position things as *I* wish.
But it is not open-source code, and I have implemented it only for
RhoMobile Rhodes, not PhoneGap.