This is because not all projects have the Default Project Layout associated and you added the tab to the Default Project Layout .
A way to check this, is to add the column "Page Layout" in the Project List.
Then in the project list you can see which projects have a "Project Default Layout" and which don't.
Only in projects with the default layout you'll see the customized tab.
Note that Page Layout is assigned on creation of the project, but if necessary, it can be altered whenever required.