They were already shopping for starting pitching a month before the sweep.
Milone has options and just pitched the previous day... Johnson was the only pitcher in the bullpen not used in the extra inning game the previous day, so they might have needed him tonight. Also, he has enough service time in to deny the assignment.
My guess is that by the end of the month Chavez is traded for a 2B/MI, Sogard is sent to AAA, Johnson is traded away for non-prospect AAA players/released, Mills moves to the pen and Milone is back in the rotation. Chavez was a scrap heap reliever turned top 20 starter, his value isn't going to get any higher from here and he was never in the team's long-term plans anyway.