Using OR controller TPS2115A
The circuit is fine, the LEDs wont affect the IC and the LEDs are probably telling you the right thing.

It sounds like its actually the camera which is keeping the power banks on, not the LEDs. The TPS2115A will repeatedly switch between the two power banks as the load will cause the voltage of the power bank to sag.

So the power banks are alternatively supplying the load and therefore staying on.