I downloaded and setup Gillion on my website (movatohome.com) the other day and I like the theme.
However, changes I save in the customizer, like changing the header background color and text color are not saving to my live website.
When I enter the customizer I can see my changes and they are saved but then once I close it the changes are nowhere to be seen.
I have cleared my cache and am using a child theme. I also tried activating the main theme and making changes there and the same thing happens.
Sorry to hear of the problem you are having.
It seems the theme generated file /wp-content/uploads/gillion-dynamic-styles.css doesn’t have sufficient permission on your server or it is heavily cached.
To resolve the issue I modified the code in the theme file inc/static.php to add custom CSS code inline in the page instead of CSS file.
Could you please confirm whether it is working fine for you now?