You can't manually put potions in the brewing stand, it's only possible with a hopper.
I tried to put a fire resistance in the brewing stand to transform it into a splash potion, but no matter how I tried it's not possible to put them inside. (shift-click, manually drag)
Steps to reproduce:
1. Brew a long duration Fire Resistance potion
2. Get it out from the brewing stand
3. Try to put it inside again
If you use a hopper at the sides of the brewing stand it works properly