Bugs get in the house during lease. Does landlord pay or tenant?

[Tim Ball]

My tenants were signing the lease today and they are moving in March 4th, 2016.  When I was going over tenant responsibilities etc.  We came to the part of pest control, etc and one of the tenants said if its her fault due to rats, bugs, etc, that they would pay for it.  But she said, "If the neighbors spray their house and the bugs end up coming over to my house, then landlord pays, right?"  

I was kinda taken back and didn't know how to respond.  "I told her I would would discuss it with some other people and Ill get back to you on that."  You guys reading this are the "other people" :).  Can I get some advice on how to respond or handle this situation?  How do you even track if it came from another property?  I dont think pest problems arent always necessarily anyones fault, its just natural that bugs can get in.  Please let me know how I should respond to this situation if it ever does arise.  Thank you.