When I add a task to a project (or to multiple projects), the project assignments are not visible to people who are not on those projects. So when they view the task, they do not see what project it is assigned to.
This is frustrating behavior, because it means that the users who have visibility into the task because they are followers are unable to see that the task has been added to a project. I fully get that they should not be able to see the rest of the project content, or see the project in their sidebar, but I think they should at least be able to see which project the task is in.
Here’s the most common condition where it occurs: someone adds a task to my team’s incoming queue project. We assess the task, and move it to whatever project it applies to. Let’s call that Project A. The person submitting the task (or anyone else following the task) then looks at the task, but can’t see that it was added to Project A, and winds up adding a comment saying, “this task should be in Project A” and we have to reply and say “it already is.” I don’t think they should gain visibility into Project A, but rather just see that the task they have visibility on is assigned to Project A.