Junior checks for updates shortly after launch and periodically while it runs, then downloads anything new in the background. You are not asked about any of that.
What you do get is a banner reading Update ready, with Restart. Pressing it closes Junior and reopens it on the new version.
Restarting ends anything you are recording. Junior asks you to confirm if a recording is running. Finish the call first, then restart.
You can check on demand from Check for Updates... in the Junior menu in the menu bar, or from About in Settings.
Questions
Can I put off the restart?
Yes, indefinitely. The banner waits. You keep running the version you have until you restart, which is fine, though you miss whatever the update fixed.
It says the update failed.
The download or the install did not complete. It will try again on its own. If it keeps failing, your firm may be blocking it, or the disk may be full. On Windows, check whether Settings says Updates managed by IT, in which case it is theirs to fix.