Your workflow needs to have "conditions" added to it.
The "browse project" permission allows users to SEE issues. The workflow transitions you are seeing as soon as that is granted are appearing because they aren't protected. If you look at the default workflow, you'll see it's got conditions on every step, like "must be a user in the project" or "must have resolve or close permission". No conditions = anyone who can see the issue can use the transition.
I'd start simple, and add "must be a user in the project" to any transition without any conditions.
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