iOS 9 has a brand new cellular settings called Wi-Fi Assist which is turned on by default. It has good intention. When Wi-Fi Assist is on, iPhone will detect when you have weak Wi-Fi signal, and automatically switch over to a cellular connection.
This is great to ensure your online experience doesn’t suffer. But it might cause you to incur large mobile data usage unexpectedly. If you do not have an unlimited mobile plan, watch out for your mobile data usage or go ahead to disable Wi-Fi Assist.
Go to Settings > Cellular. Scroll down all the way to the bottom for the Wi-Fi Assist switch. Tap to turn it off.