Yep, acrylic paints (and washes) dry very quickly. It's tough, but doable, to use acrylic washes if you work quickly and deliberately. They are not the wipe-off kind of washes. Especially if your base coat is Vallejo acrylics--they don't seem to stick well and seem to peel off easily (in my experience).
What you are probably seeing on Youtube are oil-based washes from AK Interactive, Mig Productions, Ammo of Mig, or Adam Wilder's washes. Being oil-based, they dry slowly and can be wiped off, especially if applied to a satin or gloss coat of paint.
Personally I don't like the "apply all over and wipe off" method of washes. You apply lots of the product, only to wipe off 90% of it. Seems inefficient to me, but there is nothing wrong with the technique. I prefer to apply my washes, as you say, "quickly and with accuracy." It's tougher, but doable.
I've also used artist's oil paints for washes, dilluted with odorless thinner (Mona Lisa brand). They work similarly to the Mig/AK products, but may take even longer to dry.
Some tips:
1. No matter what kind of wash you use, I suggest you allow the underlying paint/varnish to cure at least 24 hours before applying the wash.
2. Applying a gloss coat before you apply the wash will help. The wash simply doesn't stick to a gloss surface as well as a matte one, so it wipes off easier. Some will say that a gloss coat is absolutely necessary if you use an acrylic wash over an acrylic base coat, but this is a bit of a myth. When the acrylic base coat is fully cured, it is insoluble in water.
3. Mistakes with an acrylic wash can be fixed with a bit of Vallejo Airbrush Cleaner. Be careful with this stuff, it will eat through any acrylic paint. But if you use a small amount, it will remove freshly dried paint and leave the base coat intact. I dip a small round brush in a small amount of the cleaner, then unload the brush onto a paper towel. Then, using just the tip of the brush with the lightest amount of pressure, remove the freshly dried acrylic with a gentle back and forth motion. Again, too much pressure or too much cleaner and you will remove the base coat.
Hope this helps.