"Disconnect" does not mean the same as turn off device. So, that is likely why it is reconnecting -- it is not off. Check the user guide for your BT device or contact the manufacturers support.
I really cannot diagnose this properly via a forum post, but I can tell you how both my (portable) BT transmitters work with Echo. Echo is always ready to connect to BT from anything that accesses it. So, I connect to it by turning on my BT transmitter and disconnect from Echo by pressing the off button on BT device. In both cases, the Echo notifies me if it is connected or disconnected when the BT TX is turned on/off.
Same goes with my tablets and phones when connecting to Echo. If too many BT devices are left in their BT-ON state, then confusion can arise, so I make certain no other BT devices have the BT turned on. Good luck.