That does happen, a signature link does open a new tab/window. I've double checked this in the latest versions of Chrome, Firefox and Safari.
Links would only happen in the same tab/window if the URL is from the same site as the XenForo installation (ie it's an internal link) and that is as designed (it would be very annoying to have new tabs for internal links). Other than that it's an old browser or a browser extension that is causing this behaviour.
Maybe a link to the site you are having issues with would be helpful.