[SOLVED] Limiting viewing of tickets

We are just getting started with Projeqtor. We are setting up a Ticketing system for internal engineering support. We have setup a profile that is common to all ticket users.
All users are working on a single project.
We are nearly up and running but at present all our users can see and change all the tickets.
What we really want is that they only see tickets that are assigned to the respective user and all other tickets are invisible.
Various combinations within profiles have been adjusted but at present we cannot get to the solution.
Any advice welcome.
Thank you.

Thank you for that very good information.
I have followed your instruction and now have the Responsible person seeing just their tickets.
One last hurdle to cross I cannot see how to enable the responsible person to update the "Status"

OK all now solved - Workflows was the answer.
Many thanks for your help.