We were provided with an Installer for version 9.03 (1667) when I installed it a few months ago. However the latest installer that we have is 9.03 (1747), I have not yet updated to that one. However you need to specify a server URL and there are other DSN settings that need to be correct for Pulse Secure. We run an installer that is provided by our employer, who also configures our Network Settings for DNS, etc. We also use this with two-factor authentication. So your setup may be different.
This version of Pulse Secure is listed in our download area as being compatible with 10.11-10.14 (it may also work with 10.15 and the documentation just hasn't been updated to say that yet).
It might not so much be a setup/settings issue with Pulse Secure as it could be a conflict with something else running on your machine. Or as I suggested, your Network Settings might not be a proper match for Pulse Secure on your machine. It's sort of hard to tell from remote. But I think there are close to 1000 Macs running Mojave here using PulseSecure (it is mandatory to have running on every machine when used off the institutional network, which of course laptops often are).
I am wondering if you should try booting into safe mode to see if your conflict goes away. Not sure if VPN works in safe mode, but it might be something to try.