The copy will refer to the number of "counters removed this way", that is, the number of "+1/+1 counters [removed] from Sage of Hours" to pay for its second ability, just as well as the original will. For example, in general—
if five, six, seven, eight, or nine +1/+1 counters were removed from Sage of Hours as you activated its second ability, you take an extra turn after this one when either that ability or a copy of it resolves, and
if ten, eleven, twelve, thirteen, or fourteen +1/+1 counters were removed from Sage of Hours as you activated its second ability, you take two extra turns after this one when either that ability or a copy of it resolves.
When in doubt, call a judge.
Objectivist here. Hit me up to talk philosophy.
(or more than one if you removed multiples of 5 counters)
RULES OF MAGIC :
http://magic.wizards.com/en/game-info/gameplay/rules-and-formats/rules