I think a lot of your minute was up to something else (wind, rest/food in prior 24 hours, etc). Part of it was probably due to being able to recruit new muscles (do you feel a bit sore?). Your description lead me to believe that your position is much better now.

I think fit is absolutely critical if out of acceptable range. For example on Mon I rode and noticed my left foot wasn't totally comfortable when at the bottom of the stroke - I felt it was reaching a touch. Wed I checked my post, noticed about a 2 mm difference in height (based on pic of the seatpost and the logo on it when I first built bike in CA, and position there was great). I lowered the saddle, went for a ride, and my foot was okay at the bottom of the pedal stroke. Minor change, minor difference in behavior, but I think this kind of thing can eventually become problematic if left alone.

If I'm another mm or two lower, I think it'd be okay, hence my statement on "acceptable range". If I get too low then it affects bar drop, my back angle, and therefore my back. It's more comfortable for me to have the bar drop I prefer so I try and keep it at that amount.

I don't think I'd go from doing a 13:30 TT to a 12:30 TT based on a few mm difference, but I could see dropping maybe 10-15 seconds initially. The rest of it may be due to the riding conditions (wind, humidity, etc) and your own prep (food, rest, mental outlook, etc).

Whatever, a minute off is a nice improvement. Congrats!