If you are able to open the GMT window using the shortcut key and you can see the notes in the piano roll, but your edits do not take effect (no CC commands are written or velocities, etc), and also, you can not start playback from GMT's play button, is because GMT is not connected to Sibelius.
Most probably this is because the plugin key set in GMT is not matching the one created in Sibelius preferences.
To solve this:
1 Open the configuration dialog with the "CFG" button at the lower right of the GMT window:
2 Click on the Set Plugin Key button to open the Plugin Key configuration dialog.
3 In the Plugin Key configuration dialog, make sure the chosen key is the same that is set in Sibelius Preferences Shortcuts.