Hello there,
I hope you’re doing well :D.
I checked your site and the addons appear on cart page and checkout page.
If you cannot see in the order, maybe the problem is that the addons are not saved as order item meta.
Maybe other plugin or custom code doesn’t allow to add it.
I suggest you to make the following test:
Please, try to deactivate all plugins and see if the problem disappear. If so, try to activate them again one by one and see which one produces the issue.
If the problem is not from a plugin, try to activate the default theme Twenty Sixteen or Twenty Seventeen and see if you have the same issue.
Also, if you have customized files in your theme, please try with a fresh installation without customization.
Remember that if you have a plugin for the cache, you need to delete the cache before to disable it.
Please, try it and let me know.
Have a good day.