Minecraft wiki entry for Hopper, associated text: Brewing Stand
A working hopper on the top face of a brewing stand deposits only into the ingredient slot and it can push only valid brewing ingredients. A hopper on side face of a brewing stand can deposit only blaze powder or filled bottles into the three brew slots. A hopper underneath a brewing stand always extracts from the three brew slots, whether brewing is finished or not—The hopper must be locked to allow potions to finish brewing.