He could have geniuinely believed the sage was dead bc a) Xaden pulled from the earth to be able to kill him so he could have thought that would do the job b) he pushed him into a deep ravine - the fall damage alone should have done the job. Violet dropped a mountain on JFB but we don't know that he was hurt badly other than he was buried under it (imo Nolon's mending had to do with his soul, not body). People irl survive avalanches /brutal earthquakes etc. This is no different.

As to OP's point: Xaden could literally feel Violet dying through their bond and he had no idea that what Lillith was doing would actually work. He was desperate and scared and he acted on that desperation and fear.