This can be achieved in Tiki but there are certain level of complexity depending the path you choose. You have separate permissions for trackers + status items + username field or group field + user or group can see its own items.
What I usually do the most now is to restrict access to trackers interface. Meaning user don’t see the tracker view (under the hood) but the page I prepare with specific interface for a specific group or groups. Using a plugin List and some filters and you are set (more easy to write than to do I guess 😉) But that’s what I’d do.
First create an interface that do the job (not 100% waterproof)
Second set permissions to make 100% waterproof
I’ve seen that in 2 occasions; Local issues with PHP version, with a sort parameter on an item list (only on local)... May be ?