[valiant67]

It's probably not DRLs, but a headlight off delay feature.
If you turn of the ignition before the headlights, the headlights only are designed to stay on for up to a couple minutes. This was included on many of the upper trim level vehicles.
If you turn the headlights off before the ignition, the delay is bypassed. Likewise if you turn the headlights off then on again the delay is cancelled.

 

[ImperialCrown]

That is correct. It's normal and meant to light your way after dark to get you to where you're going.
See your owners manual for details. It is configurable.

HEADLAMP TIME DELAY SYSTEM

The headlamp time delay system is activated by turning the headlamps ON (high or low beam) while the engine is running, turning the ignition switch OFF, and then turning the headlamp switch OFF within 45 seconds. The system will not activate if more than 45 seconds elapse between ignition switch OFF and headlamp switch OFF. The BCM will allow the headlamps to remain ON for 90 seconds (configurable) before they automatically turn off (If the key is in the ignition during the headlamp time delay mode, then both the headlamps and park lamps (including panel dimming) will be ON). Refer to the Owner's Manual for more information.
If the headlamp switch is in the Auto Headlamp Position, the headlamps are ON due to the night signal from the CMTC and the ignition switch is in any position other than run/start, the BCM shall enter a 90 second (configurable) Auto Headlamps time delay mode. If the key is in the ignition during the headlamp time delay mode, then both the headlamps and park lamps (including panel dimming) will be ON. If the key is not in the ignition, then only the headlamps will be ON. The BCM will allow the headlamps to remain ON for 90 seconds before they automatically turn OFF. Refer to the Owner's Manual for more information.

 

[Ray Green]

Gentlemen, these characteristics sound exact so I'd say you taught us something. Thank you!!!!