How do I set the exact post date timestamp as Views contextual filter?
I think you only have to pass the hours and minutes in to your contextual filter.

I have a View with filtering between dates and the URL is like that:
http://mysite.com/myview?changed%5Bmin%5D=23-03-2013+12%3A24&amp;changed%5Bmax%5D=23-03-2013+18%3A24

This is for the access data from 23-03-2013 12:24 to 23-03-2013 18:24.

Also, make sure you have enabled the Date submodule Date views as it provides some improvements using dates in Views.