Tamiyo, Field Researcher

If a spell has {X} in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

If you cast a spell “without paying its mana cost,” you can’t choose to cast it for any alternative costs. You can, however, pay additional costs. If the spell has any mandatory additional costs, those must be paid to cast the spell.

Tamiyo’s first ability can target creatures you don’t control. You’ll draw a card, not their controller, if they deal combat damage.