JIRA grants, not restrict permissions
First, by default JIRA has a horrible permission scheme that violates security best practices by allowing everyone that can logon to do just about everything.
JIRA works by GRANTING access. You can't restrict access. By default, it grants access to the group used to logon (see Global permissions to see the "can use" groups and admin groups). This is where users are getting their access.
This may be a big effort, but it will pay off down the road by making it easy to control access.
Most of the 'old timers' use project roles. It meets the best practice for security and gives complete control to the project lead for access to their project. JIRA comes with many project roles, but you can add more if you have a special need.
Indeed, you need to get the "grant" model right first, as Joe describes.
Once you have, then there is another layer, where you can use "issue security schemes" to hide some issues within projects. This is a form of restriction, but it only works once you've got "grant" right.
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