Whenever Fallowsage becomes tapped, you may draw a card.
For the ability to trigger, the creature has to actually change from untapped to tapped. If an effect attempts to tap the creature, but it was already tapped at the time, this ability won't trigger.
This is a triggered ability, not an activated ability. It doesn't allow you to tap the creature whenever you want; rather, you need some other way of tapping it, such as by attacking with the creature.