Throughout the series we have seen Whis demonstrate different special abilities and some which we haven't seen before. Some of those would be:
- Being able to travel across Universes (The episode where Whis takes Goku and Beerus to Universe 10).
- Healing abilities and ability to create physical items like clothes.(We see Whis demonstrate this on Beerus's world during the course of Goku and Vegeta training).
- Being able to revert back time.(We see Whis demonstrate this twice after when Zamasu kills Gowasu and Freiza blows up the earth).
- We also see Whis having the ability to create an entire stadium and also undo all damages(In the Universe 6 vs 7 tournament and baseball match).
So in other words, Whis is indeed a being who possesses lots of special abilities. In terms of physical combat alone we know Whis's power is off the scale. Jiren was said to be God of destruction tier and his power alone was strong enough to shake the world of void ie infinity and Whis is strong enough to knock a God of destruction tier character like that out without even trying. If mere Namekians have the ability to create Dragon Balls strong enough to create creatures that have the ability to bring someone back to life, I don't see why a character associated with the highest hierarchy across the multiverse not have this simple ability.
So to answer your question, I am fairly certain that Beerus has nothing to do with Whis having the ability to bring a character back from the dead. Beerus has known Whis for centuries and it would only make sense that he knew the full extent of Whis's power and abilities which is why he asked him to go about doing the same.
I expected Whis to reveal this ability at the end of the show to revive both Android 17 and Freiza(When we thought he died), because the Earth's Dragon Balls can only bring a person back to life once, and both Freiza and Android 17 have been resurrected with the Dragon Balls before. So I'm guessing they didn't want to retcon that theory or have sufficient time to include the reviving those 2 with the Dragon Balls bit, so decided to have Whis use this ability considering the fact that it makes a lot of sense based on who he has and some of the prior abilities he has demonstrated.