STI is privately operated, but the employees in immigration, customs, security, drug enforcement, etc., are government employees.
My observation over the years has been that SDQ is the worse airport in DR for this type of stuff, but it does happen at all airports in DR. The other more relevant observation is that when the PLD is in power, the staff is noticeably much more professional in their treatment of travelers, than when the PRD is in power and there is blatant pressuring of travelers to give money. Regardless, my stance has always been that they can check my bags all they want, because I take nothing into the country that is illegal or that I can be charged for, so they get no money from me.