Ensure that you have configured the types of shipping groups that different fulfiller will handle. For this refer to the component /atg/commerce/fulfillment/Configuration which has a fulfillerShippingGroupClassMap property. OOTB it is configured as:
You can override this setting completely or add a map entry as per your requirements.
You can also map fulfiller names to multiple classes by listing each classes with a space in between like:
fulfiller=class1 class2 class3
Refer following documentation if you want to create a new custom fulfiller:
Once you have defined your own custom fulfiller, there are some configuration steps that needs to be followed which are described here:
Hope this helps.