It should be ordering the posts by the custom date field. If two of those fields have the same date then those should be ordered according to the post date.
You also have to remember that an ACF date field does not store a time. So today would be in the DB like this 20181211 Two posts that have today’s date in the custom field will be ordered by the post date, which includes a timestamp, for example 2018-12-11 10:34:22
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