Think of them like warm weather roaches. They can move through any sized space and will eat just about anything.
Now, as for life cycle, it is about 6 weeks. At temperatures below 50F they quickly die out. Unless your apartment complex has bad plumbing and there is a nice damp substrate, they will not breed.
My real question is are you getting lots of escapes? Unless a cricket keeper got dumped over, that seems to be a lot of animals one floor down. My wife once dumped a 1000 count box of adult crickets in the basement and perhaps three were found upstairs.
Perhaps you may want to rethink your strategy for feeding to prevent escapes.