Daytime Running Lights?
Your car might have daytime running lights, which is different than the auto lamp. The DRL feature (which is standard on Canada cars, and others may have it too (mine does)) turns on the high beams at reduced brightness all the time. It's a good safety feature and also makes for a good transition between day and nighttime auto-lamps, since the headlights are always on. You can tell if it's DRL by setting the multifunction switch to brights, and turning the headlights on and off with the headlight switch. They should look noticeably brighter when the headlight switch is turned on.
The EATC will remember the mode it was last in when you shut off the car. If you had it set to MAX fan and 80 degrees, the fan will fire up when you start the car again. In AUTO mode, the EATC usually will run the blower motor fan at low even when the temperature inside is already what the EATC is set for. This is for ventilation and anti-fogging. The off position is the only position where the fan should always be off.
The EATC has a cutout switch that keeps the fan from blowing in 'auto' mode when it needs to heat up the inside of the car and the engine is still cold. If you have the EATC set for AUTO and a temperature like 75 degrees, and it is cold outside and the engine is cold, it shouldn't turn on the fan until the engine warms up. This cutout can be bypassed by manually selecting the mode.
If you suspect EATC malfunction there is a diagnostic procedure you can do on the EATC by holding down a particular combination of keys. A search on the forum should bring this up.