Thanks for all the responses. I will definitely make mixing and some resting as part of my procedure.
As far as the hard to determine micro scale physio-chemistry goes, I want to also share another observation. I recently roughly proofed a few bottles from barrel strength to 40%. I blended the spirit and water in each bottle and did end up hitting my target pretty well. What I noticed though, is that the day after proofing, if I upended a bottle I could see mixing of the liquid inside indicating different refractive index for different liquid sitting in different parts of the bottle. That wouldn't be likely to happen if I had mixed well ahead of time, but I think it is evidence that there may be effects beyond the temperature and bubbles.
I am not sure that this is of any practical importance for now, and it may be pedantic, but I like getting into these things because it will help someone someday.
Thanks for answering my real question of how to blend properly.