Neem spray in Vermicomposting

I have a lot of little creepy crawlies in my Vermicomposting bin. I was thinking of spraying the surface with a Neem spray. My question is will it kill the flies and tiny spiders and will it kill my worms?

I shredded a bunch of cardboard, moved the wet bedding to the side and placed the shredded card board at the bottom on both sides. I let the lid off to allow more drying on the top. Then added Diatomaceous earth to top and a small layer in the middle. Less then a week latter the over moisture is going, the bugs are gone and my worms are eating... Yahhh me! By thank to Mat from Worms ect. He has been a big help.