Yes. The Mill needs a mobile smart phone to download the Mill app, and uses the internet upon pairing and setup to enable its internal clock so it can keep an automated schedule. It is not compatible with tablets.
After setup, you can operate it without Wi-Fi and without the app by starting manual cycles via the lid button. Please note that without consistent Wi-Fi connectivity, you won't be able to access some of the features like automatic scheduling, and accurate impact reports with details on how many food scraps you've added over time, etc. and the Mill team may have difficulty assisting with backend troubleshooting (if needed).