You could modify the tab opening code to force a window resize event after the tab is open:
If you have AJAX-style 'smooth' page transitions, perhaps provided by your theme, then you may find that the PDF viewer only displays at all when you load the page directly. Clicking on to the PDF's page from a different page may miss out on the initialization code of the plugin.
To be honest, we don't really feel that 'smooth page transitions' make sense in a WordPress environment where different plugins will assume a particular initialization order, so our preference would be to disable these transitions.
Please understand that we can't necessarily support custom coding solutions like these, but hopefully these notes will help developers.