Hi Gauthier,
I'm afraid that you can't filter the expense.list call by user ID to get only one staff member's expenses. For now you'd be looking at looping through each invoice in the date range with an invoice.get for it and then saving the info differently depending on the staff ID that's returned.
I'll grant you that it isn't ideal, and I will add filtering by staff ID to our list of potential additions to the API.
Cheers,
Nox