It is not suspicious and it is not crazy. The place was ready for renting as of September 1st. Why should "they" lose a month of rent because you are not ready? Either pay for September and consider renting as of Sept 1 or - if you have not yet signed a lease, tell them you have changed your mind, and be prepared to lose your deposit. Next time, realize that you do NOT get to run things. They own the place and they run the place and when it is ready on Sept 1 - THAT'S WHEN you owe rent, if you are going to rent the place.
Certified Paralegal, with 25+ years' experience & with Landlord & Tenant law experience.