I am using the final version of PrimeFaces 5.0, which means that I am using jQuery Mobile 1.4.2.
I added data-tap-toggle = "false" as recommended here (and in many other questions here in stackoverflow), but this did not solve my header problem.
<div data-role="header" data-position="fixed" data-tap-toggle="false">
, , .
.ui-header.ui-fixed-hidden {
position: fixed !important;
}