I live across town, dnprall, and my experience is that the DCT behaves poorly in warmer weather; I've never thought to correlate it to humidity. We've had so few warm days this year. ;)
I've had good luck doing some more aggressive accelerations to clear out the stumbles. Since the DCT is "adaptive", it sometimes turns itself into a hesitating, infuriating mess. I really hate driving it in stop-and-go traffic for this reason. Find a quiet, cop-free road and do some sporty launches. No need to burn rubber.
Also, holding the throttle pedal absolutely still seems to help as well. Gears 1 and 2 in these cars are very short, and small throttle changes get magnified.