Rule to update referenced node after customer completes checkout
This question seemms to be a variation of Populate an entity reference field, which suggests a solution like so:


Add Condition: “Entity has field”, checking for your reference field
Add Action: “Fetch entity by id”, supplying your node/user id from another field in the dataset and providing a meaningful name
(Note: This solution implies you get the id by a simple field value in your dataset; you might want to add another condition to register the id first)
Add Action: “Set data value”, which you now can supply your entity object from the step before (hence a name you'll identifiy in the dataset)


Apart from some Rules "Event" you probably need to add to it (related to your "After customer completes checkout"), this should be pretty close to what you're looking for.