To disable same day delivery all you need to restrict the same day in calendar to be selected by customers, to do the same navigate to very first settings page of the plugin called “ODT Management” and look for the third input box labeled as “Preorder Days Restriction:” place 1 as input value, and on checkout page the same day(today’s date) will be disabled for delivery/pickup date selection.
Still seems it’s not working? Check your site’s timezone in WordPress general settings(check below screen-shot) page and check your local timezone from where you are checking it, got the difference? Just make them same and its all.
This article is written when the latest version is 1.0.6.1. In feature release input box ordering may be changed.