It appeared to me that Julien got his hand on home plate literally a couple milliseconds before contact was made on the tag but the replay was not clearly conclusive. So I think the call on the field would have been upheld whether he was ruled safe or out. Had the play occurred early in the game it probably would not have been challenged.
As an aside, I wish the replay process would be changed. I think the reviewer(s) should not be influenced by the call on the field. The replay would need to be stopped before it shows the umpire making the call. The play would be called one way, or the other way, or inconclusive. Only if the reviewer rules inconclusive would the call on the field stand.