So here's the thing; I haven't seen Giovanni's Contraption yet! Others in my alliance say they have seen it and been able to refuel it and whatnot, but I have yet to catch it here. That said, I have gathered quite a bit of information about it, so I will put that here, so that others like me know what's coming!
Giovanni's Contraption lands in Cinder Caldera, and Giovanni needs help refueling it. Like Liang and Glurb, the "order" that Giovanni places for refueling is different each time. Also like Liang and Glurb, the variety and quantity of items he asks for seems to get larger and more difficult as you rise in level.
Where it differs from Liang and Glurb is that the Contraption's fuel gauge has five sections. Each time you complete an order in the time given, you fill one section of the gauge. When you fill the first section, the rewards are somewhat low, but as you fill successive sections during the same visit of the contraption, the rewards get better. It sounds like the boosts seem to be earned most often when filling the third, fourth and fifth (top) sections of the gauge.
I'm not certain, but I believe the time limit for filling all the sections is 20 hours. Someone please correct me if I'm wrong!