The Any.do Moment will pop up at a specific time on the days you'll set it to. Changing the preferences can be done from Any.do Settings → Any.do Moment.
Select 'Edit' next to the time section to change the time of your Any.do Moment notification. The blue dots indicate days on which the Any.do Moment alert is active, and underneath it you can set the alert time. Grey dots indicate inactive days. You can disable all alerts by tapping the 'Disable' button.
You also have the option to activate the Moment immediately by selecting 'Start Planning Your Day'.