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As m0lsx mentioned, Aphonopelma seemanni are well know for this. She's actually extended what's in the picture another 10cm and increased the height of the bottom chamber. It's a natural behavior they have for regulating temperature and humidity in their environment.
You shouldn't have any...
Believe it or not, T's actually learn complex behaviors in response to their environment. How your pets behave is partly due to how you treat them.
A couple of my T's know exactly what it means when I open the enclosure. They come running for their roaches the second they hear the door locks open.
It really doesn't matter. Once you get one T you'll instantly want 50. You'll find a way to get all four of those species before the end of the year.
Like Konstantin, I'd personally start with the T. albo as well. They're just so fluffy!
That's the thing about Aphonopelma - they all look alike at various stages. You literally can't confirm a wild-caught female A. chalcodes from an A. iodius, A. eutylenum, or A. johnnycashi without knowing where it came from and/or doing DNA sequencing. The collection site is part of the accepted...
More arboreal T's. Fewer enclosures. Problem solved.
Sarcasm aside, fly paper and electric bug zappers are your only safe bets. There are also UV light/fly paper combo things that are a best-of-both-worlds solution.
Stay away from chemicals. Some insecticides are 10,000X more toxic to spiders...