It is possible to use the shipping method selected by the customer during checkout as part of your shipping rules formula in Shiptheory.
1. When creating a rule in Shiptheory, select the Carrier and Delivery Service you wish to use and then select Custom from Does this rule map to a specific method?
2. The drop down box will turn into a text field. Type the shipping method exactly as it appears on your Shopify store. The rules engine looks for a complete text match.
3. Make any additional changes to the shipping rule you require and save.