Type of oil has nothing to do with the shifting of the transmission. I know some GM cars, the ECU is actually programmed to shift higher in colder conditions, could be normal… How cold does your part of California get? When I hear cold, I think 0-5F. Either way, you seem to be good with the trans fluid changing and if the gear changes are still smooth and quiet, I wouldn’t worry about it.
As far as oil brand goes, it’s all basically the same in my book. You’ll never know the difference as long as they’re the same weight. Just don’t use synthetics if you’re manual calls for standard motor oil