The assumption is that the coop has windows and light gets in there as well. So when the mechanism is mounted on the inside, the sensor uses the light levels inside the coop. Check your model, but you should be able to adjust how dark it needs to be for the mechanism to be triggered.
I haven't had a solar powered model, so I don't know where the solar panel is. If it's separate from the motor and can be installed on the outside, and the motor on the inside, that would be ideal, but if not, I guess the whole thing may need to go on the outside. Mine has batteries so that doesn't matter. The batteries last a VERY long time, so I personally don't see the need for a solar panel. It's nice, but for such a small amount of electricity, it's not worth it, especially if it puts restrictions on where the unit can be mounted. If you want to be more green about it, you can get rechargeable batteries to reduce your (occasional) battery waste.