They may have been walking through space, but both of them were able to close vast distances in a single step so it did not take them long at all to reach earth. They calmly returned to the school when Thoth told him he was returning to the battle worlds and that he would see him there. He vanished and Regius made his way back to his room.
Regius could tell that everyone was in the training room and, in fact, it seemed that most of them had awakened at this point, but ultimately, after everything that had happened, he really just felt drained. He felt that drain both emotionally and physically. Regius erased all trace of his presence to not interrupt them as he looked towards his bed, understanding that he could use the sleep, but instead he walked out to the balcony.