That's called a 1-2 bindup and is where 2nd applies before 1st lets go.
It's actually common for them to do it when manual shifting without a restrictor plug in the accumulator port like the Transgo shift kits show to do if the trans is going to be shifted manually and has had it's flow ports opened up for firmer shifts.
For this problem you can try backing off the front band another full turn and see how it acts. (it just makes the second gear band take longer to come on)
hopefully giving time for 1st to let go.
If it starts skipping second all together and shifting from 1-3 it's too loose.
The early 1-2 shift is pretty normal for a stock trans also, and there are a couple of things that can be done there.
Another governor or an added stronger spring in the existing governor. (that mod can be found online) and is also part of some of the shift kits instructions.
The governor weights can also be lightened to fix that early shifting.
A replacement governor made for later shifting also available online (Google search should find that)
Or you can do what I did with my stocker 904 with stock linkage that worked well.
www.letsgocomputers.com/shifts.htm
This works pretty good for no more than it takes to do it.