Hi,
What happens when you temporarily disable "CleanMart" ? Does it change anything? I am 100% sure the result will be the same, because display/hiding tabs on Virtuemart Frontpage has nothing to do with CleanMart.. CleanMart just styles it, and makes the product elemtns look good. This is actually what templates do mostly. Templates won't decide what to show or what to hide, this is being provided by the core (in this case, by Virtuemart Component) templates just makes thing look prettier.
To temporarily disable CleanMart, connect your website via FTP and rename this folder:
/templates/YOUR_TEMPLATE/html/com_virtuemart/
to
/templates/YOUR_TEMPLATE/html/com_virtuemart2/
and browse your website again. This time you will notice, your website is not using CleanMart anymore and you will start seeing the official Virtuemart page layout. Check whether or not you see those extra tabs in the VM Front-page.
Regards.