Not watered in, exactly - it needs to be watered down to the surface. With chemical fertilizers, those have to get enough water to dissolve the fertilizer crystals. With organics, all you need to do is wash the fertilizer off the grass blades and down to the surface of the soil.

So, could I put it down now and wait for the next rain or watering cycle?

Yep. For anything people think of as organic, ignoring it is perfectly acceptable. In many, many years of use, I've never watered anything in and simply waited for nature to take care of it for me.

(There's a reason for the definition above; there are organic molecules that do need to be watered in and are available as fertilizer, but the stuff you're talking about, no).

Thanks for the info you guys, much appreciated!