It works very well. On a larger scale it is referred to as plowing.

I guess plowing and tilling are not the same thing? I was told that tilling can actually spread weeds, but I guess plowing is different since the weeds are just turned over rather than ground up.

That makes sense!

Plowing is the same thing as tilling, and both can turn up "weed" seeds that might germinate.
Your mother did what many of us do with "weeds" if we don't gather them up and compost them, although there are thos neat freaks that cannot bear to see this kind of messy garden and have this strong need to throw away those "weeds" and the nutrients the took from the soil and which you will need to replace.

Don't do this with dandelions though cuz they'll sprout seeds as they die. If you want to prevent the weed seeds from germinating, you can mulch after you till it