According to the DUPR FAQ page, "Ratings are updated every week, usually on Tuesday afternoons. Our team is hard at work, and we'll be moving back to instantaneous rating updates very soon. In the meantime, keep an eye out for your updated rating early next week. Including all matches posted before Sunday night."
Once again I will go straight to the source and the DUPR FAQ page states "We receive results from our partners which include clubs, associations, tournament organizers, federations, and our very own users... The results from these events are added to DUPR every week on Monday and are updated in the App on Tuesday."
After completing my research on the DUPR rating system, In my opinion the best day of the week to check your DUPR rating will be Wednesday.
Info and image courtesy of the https://www.support.mydupr.com/