Pairing multiple iOS devices with one bluetooth keyboard

I have a Keys to go Bluetooth keyboard that I use with my iPad. When I turned off the Bluetooth of my iPad, and paired the keyboard with my iPhone, it worked fine with the iPhone. The issue is that when I turn off the iPhone Bluetooth trying pair back to iPad, the iPad doesn't recognize the keyboard. I could make the re-paring to my iPad only after my forcefully forgetting the device manually with my iPhone.

I just expected that the Bluetooth keyboard can connect any devices nearby, but this may not be the case. Is this expected behavior or Bluetooth keyboards? Is this specific to iOS devices?