[solved] Home page caching - Desktop modules appear on mobile

First off - awesome plugin! This has made a massive difference to the speed of our site and was super easy to set up, so thanks!
However, there's a slight problem that I'm struggling with ...
I have set certain modules to not display on mobile in the Prestashop back office (the key one being the default Prestashop home page slider which is content-heavy).
Unfortunately, with LiteSpeed switched on, I'm getting these modules appearing on mobile.
I've tried switching off Guest Mode, but that didn't seem to make a difference. I don't really want to not cache the whole home page (seems to defeat the object!)
I guess I could do all the mobile tweaking through CSS, but I was hoping to avoid that (and I don't know whether a display: none still loads the content anyway).
The site is here: https://accessoriesforthehome.co.uk
Any pointers gratefully appreciated,
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