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I don't know if Erik Ten Hag can replicate what Xabi Alonso did at Leverkusen it's not an easy task cause not many clubs have had such great unbeaten run but since Ten Hag has got experience in the league before now it shouldn't be a tough task for him, I expect that he should have more winning than lose bit if he fails to then he has no business in the Bundesliga coaching a team like Leverkusen. This is an opportunity to silent his critics who think he's not a good manager.
Even Xabi Alonso could not replicate Xabi Alonso, so I don't think anyone would seriously be expecting Ten Hag to win the championship.
I imagine the owners' expectations are much more modest, and probably finishing in the top 3 in the Bundesliga + advancing from the league stage of the Champions League would be seen as a success. I guess the team's playing style would also be considered. With Man United, he struggled especially with the attacking part of the game (i.e. scoring very little goals), so I hope the same won't be the case with Leverkusen under his rule.
But yeah, he definitely has something to prove and would like to show the world that he's capable of leading a top European team. I wish him all the best.