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I may be misreading your problem, but it sounds like you're looking at the wrong bulb. When you turn the switch on, the DRL lamps should be on and when you turn on the headlights, they should go off. Describe exactly what you're seeing again.
The DRLs and the turn signals both operate in the same dual filament bulb. There's a parking light on the side of the cluster. The parking lights only operate on the light switch on the stalk.
The DRLs stay off until the ignition is turned on and the parking brake is off. Then they stay on until the car is turned off. With headlights on they also turn off leaving a low setting. At any time, the T/S will operate normally.
If I read your post correctly thats whats happening?