If there's no rule saying it does, it doesn't. That's how the rules generally work- unless they specifically say you can do a thing or that something happens, you can't and it doesn't. The exception is common sense. Your DM will have to point out the specific rule saying as much or admit he's making a houserule on the fly to inconvenience a player, which is extremely poor form.
Now, common sense does say people could hear you drinking anything, including an extract, but it'd be fairly difficult, since it's not a very loud noise. They'd have to make a Perception roll, and presumably you could make a Stealth roll with the possibility of the other PCs taking aid another actions. Making it have some sort of spell-like display, however, is outside the rules. The results of an extract of, say, fire elemental form or something, would be obvious since you would turn into a humanoid made of flame, but just the act of drinking the extract wouldn't do anything until the magic started.
Thanks, man.
I'm checking with my DM now!
I want to drink an extract of illusion of calm, while I'm on the deck of a ship with some people. I am behind most of them .
Of course , if I drink a extract of barskin I imagine that everyone will notice, but a extract of illusion of calm or heroism I dont know.