When they say that's good for 15 days of use over a month, is it a calendar month or 30 days from the first use ?
It will be pre-validated for the travel period you specify at the time of purchase, such as from August 8 to September 7. The actual number of days depends on which month it is. See also https://www.ricksteves.com/travel-tips/transportation/trains/using-your-rail-pass.