When you move in they should move along...they are typically shy and do not like being around people. They like dry, dark places...storage closets...garages...etc etc...
If the exterminator has sprayed and you have traps I wouldn't worry.
My daughter got bitten by something last weekend that left a hole in her leg...could have been a brown recluse or another bug bite that got infected....she ran a low grade fever and the ulcer was swollen and itchy/painful. She was given an oral antibiotic and we kept the bite clean and covered.
I know of two people in college who were bitten one had a bad allergic reaction and her whole head was swollen (she was bitten in her hair) and we rushed her to the ER. She was fine after a few days. The other girl had a small reaction, her arm was swollen where the bite was and she got flushed like a sunburn. The doctor at the campus clinic treated her and she was fine in a few days. Not all bites make huge scars, but some can...
Good luck...living in Texas I have never thought much of them other than yes they live here too and we keep an eye on all bug bites...