Domain analysis - why OFF points are inside of the domain when the border is open

I have asked on a few other sites, no response but it must be something silly as many authors mention in their books.

Here is the best text I found:

My ultimate question is: Why the OFF point lies INSIDE the domain when the border is open. If it is about being off the border, why cant it be outside too?

EDIT: THank you for your answers. I found another contradicting article, what do you think?

According to the description, the INCLUDE gravity is when t>=1. However, for the other open domain, OFF point is OUTSIDE the domain, contradicting what you all and the other articles I quoted mentioned