Yea, that's a real issue then. Shoudl not be 3-5 seconds
Bluetooth has always been a janky beast, between versions, chipsets, supported profiles, etc. etc.
It's sometimes tricky to isolated whether's the phone BT or the vehicle BT.
One way to isolate it the issue:
1.) Get a stand-alone Bluetooth Transmitter/Receiver (search Amazon)
2.) Turn off BT on phone, and plug it with a wire to transmitter, and then pair the transmitter to the CX-9. Test. If you get same result, the issue might be the CX-9
3.) Do the reverse; pair the phone to the transmitter/receiver (and unpair both from CX-9), and wire the transmitter the AUX port via cable. (You may have to switch the bT transmitter into receiver mode). If you get the same result, it could be the phone's BT