By default Volusion will not include the product option variation in the output file.  The Enable Options Inventory Control checkBox needs to be ticked. 

The option products will then be added to the csv out put that can then be loaded into the Linnworks mapping tool as documented in the Volusion Inventory Mapping documentation page

Although not esential the new variation SKUs in Linnworks should be assigned to the variation group that represents the Parent product. This can then be use when listing the items on other channels via Linnlive.