Alright, White Mushrooms...where to begin...?

First off, they're pretty useful. You may not realize it yet, but they're good to have around. As you've seen, by using a certain spell at a certain time, the Mushroom gets excited and you get 1 Tech EXP. Now, to really reap the rewards, you must use that spell at the right time 3 times on him. So, if he shivers, use Fire. Next time he shivers, do it again and get another 1 Tech EXP, and then again for 10 Tech EXP. He'll drop X Arts (where X = type of magic used on him three times), a gem related to that spell (for Fire, you'll get a Blaze Gem), and there's a chance he'll also drop Mystery Goo, which is used at the Item Synthesis shop at Traverse Town to help get some good accessories as well as Sora's Ultima Weapon.