No they're not. Just because they use the Euro doesn't mean that they are members of the Eurozone.
They have adopted the Euro as their sole currency, which means that in an informal capacity they are part of the Eurozone; in that they are subject to the decisions of the ECB monetary policy but have no influence in it, being non-members of the EU. It's unilateral of course, but it seems to be a comfortable arrangement.
El Salvador uses the U.S. dollar but they're not a member of the United States.
They don't have to be, of course. Any country can use it if they want to.