The Court originally declined to vacate the stay in a 5-4 decision. The fifth vote was from Kavanaugh, who wrote that he thought the stay should be vacated, but wasn't voting to do so because the moratorium was about to expire anyway. That concurrence is certainly informative, but doesn't override his actual vote to maintain the stay.
The second moratorium was quickly overturned, with Kavanaugh voting this time in accordance with his opinion. In any case, the administration did actually follow that ruling.
The Court originally declined to vacate the stay in a 5-4 decision. The fifth vote was from Kavanaugh, who wrote that he thought the stay should be vacated, but wasn't voting to do so because the moratorium was about to expire anyway. That concurrence is certainly informative, but doesn't override his actual vote to maintain the stay.
The second moratorium was quickly overturned, with Kavanaugh voting this time in accordance with his opinion. In any case, the administration did actually follow that ruling.
This is taken directly from the actual decision (the first round is discussed on page 4): https://www.supremecourt.gov/opinions/20pdf/21a23_ap6c.pdf