Ask follow-up questions in a short interview
After a shadowing session, it might be important to conduct an interview in order to understand better why certain actions happened. This can be especially useful for actions that you don't understand or find particularly interesting or intriguing.
This interview can happen right after the shadowing session, or days later if people recorded themselves and you weren't there live as they were performing the actions.
A good question to ask
Such interviews don't need to be especially long and can basically start with the same question: "Can you tell me why you did this particular action?"
Make a synthesis
Obviously, as with any research method, once you have done several shadowing sessions, you will need to analyse what you have observed and transform it into learnings that will help shape the service, product, or interaction you are designing.