When you say "turned on" do you mean you turned the temperature control from cold to hot? If so, it is likely that the hot water flow control valve is stuck open, even though you are now wanting the system to blow cold air. The problem is likely to be that the AC coil simply cannot over come the heater core (both are in the same air stream) being fed with 200+ degree water. This assumes your AC compressor is working and engaged.
The simply way to test my theory is to use two pieces of flat wood (like a paint stirrer) to protect the hose while you CLAMP OFF the hot water hose to the heater core. If the other hose coming from the heater gradually cools off, and the vents begin to blow cool air, then you have proved the hot water control valve, which is operated by the dash controls, is stuck open. You can either fix it or replace it. OR, you can install a simple ball valve in either heater hose to ensure the hot water isn't circulating unless you actually need heat. This method has been used by many, but it lacks the convenience of the "adjustable" valve connected to your dash controls.
2016 EC Aspire 42RBQ / 2014 CR-V