YES
Only difference between 'manual' and tow vehicle activating trailer brakes is when using tow vehicle brake pedal trailer braking is proportional.
When using the 'manual' lever the trailer brakes receive FULL battery voltage
Trailer brake lights function in either mode
Per Tekonsha
That's actually part of how the brake controller is designed. It does that so that if you were towing a trailer and you were applying the manual override to slow yourself down without touching the vehicle brakes drivers behind you would know that you were slowing down. Its a safety feature and everything is working as it should.