non-duty days away from home base
 

How are non-duty days (required for rest) normally counted in regard to monthly duty days when out of the home base? As off days, rest days, duty days..?

(EU-OPS)

Well, normally, days off should be taken at base but are you referring to minimum days off required at base, per month, or rest periods, days off, away from base?

Depending on the applicable regulations a crew member may agree to a temporary basing, but often regulations stipulate that a crew member may operate a maximum of circa 7 days before requiring a day off to thereafter continue duty days, often that day off may be anywhere but there should be a stipulated number of days off per month at base unless otherwise agreed.

Yes, legally required days off can be scheduled away from base but you still need your monthly, or whatever, days off at base depending upon the regulations.

Day Off Down Route or DODR on the Crewing System.

HOTAC still provided and per diems paid, everyone is a winner.

Aren't they?

Not if you desire to take your days off at home with family and the company would prefer (prefer=insist) you to take them downroute.