Digital timer rated for incandescent load only -- what would happen with a small motor load?
I will answer the bonus question.

The filament of a lightbulb has a low resistance when cold and normal resistance when hot (so do all metals, but wires etc usually do not heat up enough for the change to be noticeable). Which means that when you turn on the lightbulb, the filament is cold and has low resistance, so the initial curent surge is very high (tens of amps), then the filament heats up quickly and its resistance increases, reducing the current.

Your device probably has an output driver that would not tolerate to inrush current of a big lightbulb (or a CFL or LED power supply).