Change the color of the icon in the top bar to green when a new review comes up.
We already have a red dot indicating there are more reviews than normal:
It's not feasible to reliably notify individual users of new review tasks, because their availability depends on various factors:
- your reputation (some queues require more reputation than others)
- whether you've interacted with the post already or not
- how many reviews you already did in a particular queue
- if it's your own post or somebody else's
- if you've used your maximum daily up- and downvotes or close votes
As for an alternative solution, years ago I frequently used a userscript Review Stalker Reloaded; I'm not sure if it still works, or if there are other options.