It's not a bug, it's a deficiency in the design of their service.
On your phone, go into settings -> messages -> Receive At -> Caller ID
Set this to your AppleID, or any email that you configure to receive at both devices.
When you respond to a blue iMessage, their end will pick up on that, and shift response path accordingly.
You have to start a conversation with your phone, but you can continue it on your iPad.