As Thomas Adrian says, your problem could be that only the current tab is not sent to the browser with the XPages tabbed panel, so any client-side javascript event (e.g. a partial refresh that does not update the server or anything) will not update your field. You can see this in firebug, by checking the requests to the server, or by viewing the source HTML. All this means you can't use client-side javascript to update a field on a different tab. You may be able to use SSJS in a partial refresh, so getComponent("myInputText").setValue("new value"). However, because you're on 8.5.1, you'll hit any validation issues.
The basic dojo tabbed panel sends content for all tabs to the browser, but just hides the other tabs from view, so it would allow you to update the field with client-side javascript. The dojotoolkit website will give you the syntax to use and the dojo modules to include, but it's quite straightforward.