Winds could very well have been a factor. There are maximum allowable wind speeds for formation takeoffs.
As for the standard order, I've always seen it just the opposite of what you mentioned. Usually the diamond-four followed by number six doing a quick roll with a turn-out, then number 5 pulling into an immediate loop. However, the team obviously retains the right to alter the show however the commander sees fit and approved by his immediate commander.
By the way, when I was stationed in San Antonio, I had the opportunity to listen to the Thunderbirds frequency while in the tower. Normally, they do not disclose their frequency for safety, as they rely heavily on radio transmissions to coordinate. Unknown radio calls would disrupt their routine. However, our "air boss" for the show was a former Thunderbird and he was able to get the frequency. At times, these guys are pretty funny. They sang a song as they taxied out...each pilot took a line, and they are very animated in making their coordination calls. If you ever get the opportunity, they're a fun bunch to listen in on.