Wow Annie, Tuesday does appear to have picked up her enthusiasm and is searching well, especially that you had already completed 7 samples. Well done.
Great first search. One cue and she was off, so she certainly understands what you want her to locate. When Tuesday locates a sample, are you after an active or passive response. The PNW Truffles are quite fragile, and an active response may damage the truffle and reduce its quality.
BRILLIANT that you are down at her level now, and also that you asked her to relocate the truffle once you were down there. She had obviously placed it in a safe place and had to relocate it so that was excellent work. Your encouragement during this was spot on.
In a previous comment I suggested you reduced the number of throws after you locate samples/truffles. I also meant to suggest changing throws to tosses. The reason is that the forest, at present, looks very clear. However, there can be unknown obstacles under leaf litter which could cause harm to your dog. Also as you get deeper in the forest it will become more dense and chances of free areas to throw a ball will be reduced. To keep Tuesday safe, I would suggest tossing the ball to her mouth a couple of times rather than throwing it away from you.
Tuesday did an EXCELLENT long search for the second sample. It was interesting watching her body language, and encouragement may have assisted her at this time. Each dog is different in regards to encouragement, and the only way you will know if it interferes with her work is to test it out. In one session you may want to talk through one difficult find, and then not the other; give differing amounts of encouragement (continual talking to just occasional comments), and different volumes (loud to quiet). Review the video and see if she finds it quicker or slower when you are offering encouragement. At 1:38 you supported Tuesday in her hunt for the sample with encouragement. Did you start encouraging her because of the change in body language or because you knew where it was hidden? Ooops. Sometimes they just decide to do their own thing with the sample/truffle, but you handled this really well, no panicking or rushing after her, these things happen.
If Tuesday has a secure indication, then the opportunities for her to remove the sample/truffle will also reduce.
The last search was GREAT as she went away from you and searched. Try not to lose sight of her though as you could miss out on so much of her language, and you never know she may find a real one whilst you are not watching! However the other can be said about hanging around the samples. If a dog is only successful when you are standing near or next to a sample then you become part of their picture to success. In this instance, other than a brief disappearance, your last sample find was brilliant. Both of you are charging forwards with developing your truffling relationship. You are doing very well.