To clarify the issue: In the post (or page editor), click the [Add Media] button, then you get the ‘insert media’ popup. Without the plugin the ‘Media Library’ tab is selected, with the plugin active the ‘Upload Files’ tab should be selected.
Is the issue you are reporting that the ‘Media Library’ Tab is selected?
If so, we need to find out the reason why it isn’t working for you it works on all of the sites I have tested it on. Once we have a reason there should be a way to fix it for you.
Is the plugin showing as active in plugins -> installed plugins?
Which theme are you using?
What is the URL of your site?
To rule out a possible conflict with other plugins can you temporarily deactivate all other plugins and try again?