With Rek'Sai Burrower, when revealing a unit, do you need to pay the cost to play the unit?

Yes, you must pay the full cost of the unit when using the Rek'Sai (Void Burrower) legend ability.

According to RiftJudge FAQs #9823, #9215, and #284, you are required to pay the card's energy and power costs as normal when you play it using this ability. Only effects that explicitly state "ignoring its cost" allow you to play cards for free. Because Rek'Sai (Void Burrower)'s ability does not include this phrase, you must pay the full cost to play the revealed card.