"1 cup, drained" - does that mean measure before or after draining?
Drain them first.  Your concerns are spot-on, and if you measured and then drained them, you would end up with less than 1 cup of yams.  Generally, you can tell be cause the recipe called for 1 cup of drained yams, not 1 cup of yams in their sauce.

Drain them, but double check that you won't need the liquid for anything later on in the recipe... That's a mistake I've made too many times with canned foods.