I could be wrong, but it seems that when a file is opened in HTML5 web version, the export data option (represented as a cloud icon in the top right) for each data view is only available when the view toolbar is set to show (rather than e.g. pop out) for that view.
If I'm wrong, please let me know what I should be doing differently. Otherwise, I think it'd be useful if these two functions were uncoupled - for example it could be problematic if I wanted a file to be viewable by end users both in HTML5 web version and in the Omniscope Desktop IOK free Viewer version, since either the web version user would be unable to export data or the Desktop IOK free Viewer user would see a more cluttered presentation. It's only a small thing but would make life a little easier.
You are correct, this is a current limitation - all the menus are hidden or shown based on a single option and we just support visible or hidden... We will improve this behaviour in future.