If enabled for your project, on each page of the CMS you'll notice a Sync to Web button at the bottom left. Clicking this will trigger a sync for your content changes to be reflected in the online/cloud version of IdeaLayer. Just remember to press this any time you want to check your changes using the cloud version.
This step is not necessary (and you may not see the button at all) for publishing your content changes on the Engine (desktop) version of IdeaLayer.