That's normal. In fact, the Court will not doubt hear oral arguments in several cases that day.
This isn't a trial, and there will be no witnesses. This is only oral argument. Each side will argue it's position, and the lawyers will be asked questions by the Justices. This is only a small part of the record upon which the Court will rule. The Court will also have material from the transcripts and records from the proceedings in the lower courts as well as the briefs (written arguments) submitted by the parties. Following oral argument, the Court may also ask for further briefing on particular points.
The decision probably won't come out until June, at the earliest.