The instructions are right. Moving air feels cooler so you want the fan to blow down on you in the Summer. In the Winter you don't want air blowing directly on you, so set the fan to pull air up. That way it moves the warm air down the walls without the chilling effect of a direct breeze.
Getting a good fan can be tricky. Aside from air-movement issues, another problem with cheap fans is they tend to be noisy (60 Hz buzz), especially at slow speeds. Though that's generally not a problem in a working garage.
I have two fans I've been dragging with me from rental to rental for the last 20+ years. A cheap Monterey Fan "Hi-Tech" 52" I bought at a big box in 1986 for probably $40, and a Hunter Infiniti 52" I bought for $100 about 1994. Both move lots of air and make no discernable motor noise.
The house I rent now came with two ceiling fans, one appears to be mid-range 52", maybe a Hunter, and the other a cheapo 42" ceiling-hugger. Both are terrible at moving air and make horrible humming noises on low speeds.
Which all comes back to - cheap or expensive - ceiling fans really have to be tested to prove their worth buying.