Actually, I have egg cartons in 1 of my drawers and they are all over it all the time. Both worm and beetles. I am sure some of the eggs will be laid on there (in my bin).I finally gave up with my mealworms experiments, I have a TON of them... I just dumped them all in a kinda big tote and gave them some baby carrot chunks to munch on... the room they're in is pretty humid too so I'm not worried about them... I've got a 20 gal fish tank in there and it has lost 3 gal in less than a month to evaporation so all that water is going into the air in that room... One odd thing they did, I tossed some cardboard egg cartons in there with them and a bunch of them (20-30 at least) climbed up on top of one and snuggled down in one of the dips in a big pile... I started worrying if they could get out, so I dumped them all back down in the bedding, I'll see if they get up there again...
That is how 1 guy separates his live from his dead and pupa. He just dips the carton, they crawl on and he transfers to their new bins.
So it is completely normal!