Ok. Instead of talking in general here, give us specifics. Do you have the factory speakers installed in back? Are you going from OEM JBL to aftermarket? Etc, etc.
What is the brand / model number of the aftermarket radio you installed?
What is the brand /model number of the amp you are installing?
Speakers?
Did you use a wiring adapter when you connected the deck to the OEM wiring?
There's no real turning off of the internal amp guys. If you don't have anything connected to the high-out (speakers), it doesn't see a load. It's not suggested to have speakers connected AND RCAs as this can cause the ICs to burn out, But in all my years installing it's always been just one or the other (connect speakers OR amp RCAs). No switching of internal amps on & off. Not to say there may be a few out there like that, however, MOST you don't need to do anything other than connect it correctly. Now, I'm not saying I am absolutely right, and you are wrong. I do remember an Alpine I had many years ago that you had to switch the EQ setting from deck to AI-Net if adding an external unit. Anything is possible. Which is why I'm asking for model numbers etc.
Anyway, how are you inputting the front audio signal to the amp? Are you using the high out input or low out (speaker level, or RCA)? If it was high out you would have used the white & white/black and grey & grey/black wires from the deck to the amp. If you used RCAs, you should now cap these wires out of the deck with heat shrink or tape because they won’t be used.
The green & green/black and purple & purple/black wires should be wired directly from your deck to the rear speakers. If there was a JBL amp in the system, bypass it by running your own wires to the rear speakers from the deck.