Turn alerts on for each device you use. On an iPhone or iPad, add Unison to your home screen first — Apple won't send them to a browser tab.
Two things tell you someone is waiting on you.
In Unison — the Requests item in the sidebar shows a filled number. That works everywhere, on every device, with nothing to set up. (Requests are on the Plus and Pro plans.)
A pop-up on your phone or computer — on the Plus and Pro plans; switch it on in Settings → Notifications. Do it on each device: your phone and your laptop are separate, and turning it on for one does nothing for the other.
iPhone and iPad — do this first. Apple only sends alerts to an app on your home screen, never to a browser tab. Open Unison in Safari, tap the Share button, choose Add to Home Screen, then open Unison from the new icon and switch alerts on there. Until you do that the switch isn't offered, because it couldn't work.
Nothing arriving? Send me a test alert, under the switch, reports pop-ups and email separately:
Alerts are never sent late. Turning them on doesn't deliver anything from while they were off, so test with a fresh one rather than waiting on an old request.