PDF support on mobile devices lags quite a bit behind what you can do on the desktop, and it always depends on what software you use. The default PDF viewer on iOS for example does not support any interactive features. But, when you open the PDF file in another viewer, all of a sudden, you see more features. Which PDF viewer are you using on your mobile devices?
Adobe's Reader for iOS would also not show the signature field correctly but allows you to sign with your finger via the "Freehand" tool, Readdle's Export PDF does show the signature field, but also only offers you to sign with a pen, but does allow you to store your signature.
Karl Heinz Kremer
PDF Acrobatics Without a Net
PDF Software Development, Training and More...
http://www.khkonsulting.com