For me, it was immediate.That is correct. I have received the "Sorry you did not win" text for each entry I have texted FYI.
On that note, for those that have won via text, how long did it take for you to receive the winning notification text back? I sent a text at 6:35PM EST, but have not received a text back yet. With my luck, the system probably glitched out on me at the winning time, but still have hope!