TTT can send push notifications to your device when there are new pairings available in an event that your registered user is a participant in.
Currently this is not supported by iOS devices, you can see the compatibility chart here https://caniuse.com/#feat=push-api
When you're logged in and viewing an event you should see a notification like the one shown below.
Selecting allow will trigger the browser prompt to confirm you are happy to receive notifications from tabletop.to
When new pairings are available you will receive a notification.
Clicking the notification will take you straight to the results submission tab of the event.
To disable notifications, you can update the site settings in your browser.