Typically, I crush the night before brewing.
I never crush directly into my tun.
I always crush into a bucket, lined with a bag.
I found this method to be a good idea, on two occasions...
Once, a bolt fell out of my mill base & dropped into the grain.
With the bag, I could easily reach in & pluck out the bolt...
Without it, I would have had to sift through a hot mash tun.
(I always slowly add milled grain to a tun of water, to avoid air pockets & dough balls.)
Another time, my mill bound up & I couldn't get it to continue grinding, without a susbstantial amount of time spent on cleaning & maintenance.
Had I ground into my tun, my mash would have already been started & be too hot, for a correct mash temp.