since the secondary chain is driven off of the intake cam, does it change the exhaust cam timing when the vvt solenoid operates?

 

Only intake, not the exhaust. The VVT unit operates indepenently of the secondary chain. There is a hard timing from the crank to the intake sprocket to the exhaust sprocket, but the intake cam itself is fixed to the VVT. There are two types of VVT - an earlier version on the AJ26 and a more refined version on the AJ27.