Yes, you have to use the regular potion shop if you want it to register for your count of items under "get it off your chest." Using the Toadstool one doesn't count, so I doubt that any of the other ones do, either. I don't know if you can still get prizes from the other types. I am only saying that it won't add to your count under the goal.
On another note, I really need to pay better attention to what I get in drops and from chests. I opened some mystery chests and saw coins tumble out, so I assumed that was all I got. Then all of a sudden I realized that I had 30 energy when I had been down to about 5. So one of the chests must have given 25 energy?!? Or maybe multiple chests each gave me 5 or so energy. I don't know. But it was much appreciated!
ETA, my best drops seem to be from my ducks, but ducks are not listed as being part of the event.