Content that is dripped to members becomes available at 12 AM on the day of, and everyone receives access at the same time.  

There are MemberMouse settings to choose whether you want this to be based on your server time or the local WordPress time zone settings. You can adjust the MemberMouse settings by going to General Settings > Other Settings > Content Protection Settings (found about halfway down the page). 

If you choose to 'Use local time', the local time can be adjusted in WordPress Settings > General > Timezone.