That is an excellent question.
In the beginning it might be helpful if you did just that (and that is exactly what they will do in your NW class), but almost always it has nothing to do with the scent in the pot, and more the dog figuring out what behavior gets a reward. They think, “hey I tip over pots, I get cookies”. If this is a continual issue then yes, I would suggest keeping the odor in one pot, to eliminate any doubt on your part and eliminate scent contamination. (This comes up in later lessons) This is very very common with dogs in the beginning stages as they learn what behavior chain triggers the reward.
There is a caveat to all this:
Because truffle hunting involves practical application it isn’t really detrimental either way. There will be trace odors of the truffle all over the room, along with your scent, any other family members, food from upstairs etc. There is no way outside of a clean room to create an environment devoid distractions. Most dogs can handle this stage and level of distraction easily (we do recognize not all however). The goal is for Lola to find the one that is the strongest odor, as opposed to trace amounts, and alert on that. That is why repetition and training over a long period of time is key to success.
In application in the wild, truffles are located underground, and that causes scent to move in erratic ways. You want Lola to eventually be able to pinpoint and mark the exact location of the truffle, not a foot to the left where it smells like truffle- because the whole forest will smell like truffles to her. You want to teach her to Alert at the source. THAT is one of the reasons you really want to try to reward “At the source” is to strengthen that connection between the odor’s physical location and reward.