Actually, I'm going to answer the question without knowing what type of tank you have. If you have a glass aquarium, you will get a larger death rate. Secondly, you shouldn't be spraying water in the crate. They get their water from the vegetables/fruits you give them along with the gutload you should be feeding them.
Here is the best way I've found on taking care of crickets with miminal die off AND inexpensive too.
1) Buy a rubbermaid tub at Walmart or some place similar that has a lid.
2) Cut a hole on top of the lid (I will post some pics below) and get some screen to cover the hole.
3) Cut some circle holes on the side of the tub, which tubes can be placed in for easy capturing of the crickets. I take the tubes out and then shake them in a cup for easy feeding.
4) Give them lots of carrots, oranges (but, I've found the fruit flies a pain and don't use often) lettuce, celery, eggplant (lol... I found by accident the crickets love eggplant), and any other type of vegetables for their water intake.
5) Find a good gutload.... I use Roach Coach from
www.coastalsilkworms.com.
Here are some examples of a home made cricket container:
This works very well for me.... Hope this helps!