You tap on the second (or third fourth etc) and it asks if you want to pay 2 (then more each time I think) diamonds to activate this task (as well).
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Yes, activating as second booster uses two diamonds, a third booster needs another 4 diamonds.
ClashofHolmes mentioned an important fact about Tom. When you hire him, he brings you 9 of the requested item, then he sleeps for 2 hours before you can send him for another item. That has always been a sore spot with farmers who wanted to sleep at night without setting an alarm to take advantage of every run Tom could possibly make for their diamond expenditure.
There was no way to speed up his nap until the boosters were introduced. However, the boosters that speed up his time require that you have hired him first. For example, I have 2 boosters that would speed up Tom's time, but I don't currently want to spend the diamonds to hire him so that I can use the boosters. The "hire Tom free" boosters--especially the precious 13 hour ones--seem to only be available as Derby prizes. I haven't gotten one since I began opting out. Since it costs a minimum of 15 diamonds to hire Tom, I would always "invest" 5 to shuffle my Derby prizes to try to get the free Tom booster (and special expansion permit scrolls).