Re: OSX- can't use any internet after I connect with PulseSecure
Without being able to look at your log files and without knowing more about your environment, it's difficult to guess what might be going on here.
That said, Apple did make subtle changes in the keychain in OSX 10.11 (El Capitan) that caused certificate-based authentication to fail with Pulse. This issue was fixed in Pulse 5.1R5.1. So, you may want to upgrade to that version to be safe. But if, on the other hand, you are not using certificate auth, then you may want to create a case with Pulse Secure's Global Support Center so you can share your log files and other information so a proper diagnosis can be made.