No, it enters the battlefield under the opponent's control and is not even momentarily under your control. If you both had Warstorm Surges, it would trigger theirs and not yours.
"As (this card) enters the battlefield" is a replacement effect that altogether changes how it would enter the battlefield. In this case, it replaces the card entering under your control with entering under theirs. This is like how a Mistcutter Hydra does not enter the battlefield as a 0/0, then gain +1/+1 counters (it would die) — it enters with those counters and, from the rules' perspective, had them all along for as long as it was on the battlefield.
We can check this in the rules for replacement effects:
614.1c Effects that read “[This permanent] enters the battlefield with . . . ,” “As [this permanent] enters the battlefield . . . ,” or “[This permanent] enters the battlefield as . . . “ are replacement effects.
It would trigger your Warstorm Surge (and not an opponent's) if it instead said:
When Xantcha, Sleeper Agent enters the battlefield, an opponent of your choice gains control of it.
... because that is a triggered ability that would have to go on the stack and resolve first, after Xantcha enters under your control.