If you read the opinions, it's even less clear. The majority does not make it at all clear whether or not refunds are due, and Kavanaugh's dissent specifically calls out this weakness in the majority opinion.

Even if the executive branch's actions stop here, there's still a lot of arguing in court to do over refunds.

The executive branch couldn't so much as order me drink a cup of tea unless it first drafted me into the army or declared martial law.

Why does that seem more likely? They haven't done that yet.