Reply To: Restricting date-from to current date + 1 day

It only means the current time zone in terms of the selected city/option in the general wordpress options.

To disable the current day you can add it to the array of unavailable days in /lib/modules/styles/styles.php on line 56.

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1
?>easybookedDays[ID; ?>] = [, ""];<?php

should work.

No there's no option to set the current time in these shortcodes right now.
Regards feryaz