Hi Gilles,
Thanks! :)
I created a custom HTML module titled "test". If you publish it and check in the front-end, you'll see that its class suffix does show up.
I also tested the new module that you're using and it also displays the class suffix on a test site.
My recommendation would be to uninstall the module, then reinstall it. Try the class suffix with the default settings for the module and see if it works. If it does, then try adjusting your settings to how you'd like them and check again. If it doesn't work after re-adjusting the settings, then you know that's the reason and you can narrow it down little-by-little to the actual setting.
Kind regards,
Nick