Since it can do push notifications, prob some telemetry phones home to corporate around user agent/ip, minimal fingerprinting like that.
This part is interesting, future feature, wonder how they detect that on a personal device:
“ Jailbreak detection
If a user installs SecureAuth Authenticate on a jailbroken or rooted phone, SecureAuth will detect the occurrence and will not allow the user to set up a SecureAuth account. (Coming Soon)”
Ultimately, read your AUP and BYOD policy and see what you did/did not sign away wrt monitoring on personal devices. Quite likely you can raise an HR stink if this app had more than just basic telemetry and they mandate it to be on a personal device.