Hi,
The typical pattern if you have one supporting edit page in addition to the module is to redirect back to the CMS page after updating the data and that would make it reload the data including the new data.
So after you process the button click to save the data you would do something like:
WebUtils.SetupRedirect(this, SiteUtils.GetCurrentPageUrl());
SiteUtils.GetCurrentPageUrl is determining the page from the pageid parameter passed in the url for your supporting page.
It is more complicated if you have more supporting pages, for example in the forums we don't redirect back to the cms page we redirect back to Thread.aspx passing all the needed params after a post is edited.
Hope that helps,
Joe