Well, the same way anyone knows if you break other laws. You get caught. Just one nosy neighbor who catches your kids outside during school is all it takes to get the school superintendent calling you to see why you arent enrolled in school. Then getting in trouble for not reporting or whatever it is they require. Why risk it? I would just jump through whatever hoops I had to until I got back home.
Not sure if anyone would actually know, unless people got nosy and started asking questions. If you can prove that you are only there a few months then it should be no problem. As for me, being military, I'd love to use AZ as my homeschool laws, since that is our home of reference. Since we don't actually live there and are stationed else where, we have to use the state we are living in. If I didn't use an association and people started asking questions about why my daughter isn't in school, I could be in trouble because the base will not say that we are using our home of reference for homeschool laws.
I'm just curious how they would know. I have a friend who HS her daughter here in NC. She was asking me how would they know if I were to use NC vs whatever state we may be living in for a short period of time.
No one would know unless you cross paths with some nosy people. If your child has never been registered in public school or registered as homeschooled in the state you will be living temporarily there would be no record of your child there. To be completely compliant I would consider contacting hslda.org so you aware of your rights and responsibilities.