Hi,
We have not realized this kind of problem yet. The plugin works without problem for Variable products in our test environments.
The PRO version (that uses similar technology) also works for variable products, for example on this page:
http://webshoplogic.com/product/woocommerce-custom-tabs-pro-plugin/
It may be a special problem on your site.
Can you send us your site URL to see the problem?
Thanks,
Peter Rath
WebshopLogic