Thank you all for your replies. Probably I should have been more specific.
I installed a passive keyless entry and a start push button. This means when I get close to the car, the doors get unlocked automatically without me pressing any button on my remote and when I get far from the car, the doors get unlocked automatically. I can also turn on the car by pressing the button I have installed.
The other strange behavior is, when I turn on the car and put the car in Drive mode, the daylight running lights turn on even when the light knob is on "Off" mode.
The part that surprises me is, I have not touched any wiring for the lights. These are the wires that I had to connect to my new system: ignition harness wires, the trunk wire, the horn wire, foot brake wire, lock and unlock wires. That is why I'm not really sure how can this device affect the way lights are working!!
Is there anyone here that has installed any passive key less entry that does not have this issue? I would like to know what system they have installed. Seems like the one I have is confusing my lights.