How does the date filter Last Week or This Week work in reporting? Is it Monday - Sunday? Or Sunday - Saturday? And does it use the time zone configured for the organization or for the individual user?
For reports on SFDC objects, we send the filter literal(last week) to Salesforce and then show the data which salesforce returns. Here is an article which describes how Salesforce handles that.
For MDA, we have a fixed Monday to Sunday (Standard week) definition for the week literals. Regarding the timezone, we use the timezone which is configured at the organization level, not individual user level.