the special optional rules seems clear : When they declare a charge they become Unprotected but
gain the Fleet of Foot and Melee Expert characteristics (and can declare the charge at skirmish movement distance).
Now the opponent has a charge only TUG and was first to declare a charge and so charge and shoot shoot . As the DC qin TUG hadn't declared charge at that time we assumed that it was still protected
Correct or not ?
Correct.
If the opponent waited until after the Qin had declared the charge, then the shooting would be at unprotected. The order of declaring the charges is significant in this case.