This question was recently asked in another forum post:
Long story short, there was a fix in the Pulse desktop client 5.0r8 and the Pulse Connect Secure gateway 8.0r8 to address this issue. The ticket number is PRS-303538 ("Pulse will not use Server side proxy when resource accessed from IE11 after tunnel established due to changes in IE11 application, works if resource accessed from FF"). I recommend that you ask your system administrator to upgrade to at least PCS 8.0r8 (and, really, upgrade to the latest 8.0 version that is currently available).
If you have questions about this, feel free to have your sys admin reach out to the Pulse Secure support team.
If you have questions about this