Im gonna give them a call but my question is this. Does the liability only cover you from any damage that occurs to the students aircraft?
No, liability covers you for damage to other things/people.
Hull coverage pays for damage to the airplane and is an added cost.
Lets say you're giving dual to a student and while you're screwing around with your iPad during taxi out your student smacks the wing tip into the tail of a Cirrus sitting on the ramp. Guess who's likely to get sued? That's where your liability coverage might come into play.
Now, lets say you're demonstrating a cross-wind landing when a gust drifts you off the runway and you eat up a couple runway lights with the prop. Now you get to pay for an engine tear down. Your liability coverage doesn't do anything for you (well maybe it pays for the lights you ate). You need hull coverage.
Remember your CFI policy should also cover you for personal use of non-owned aircraft, so if your buddy lets you borrow his Cub you have coverage. It acts like the renters insurance that an FBO would recommend (or require) renters carry.
You might not need $50,000 in hull coverage when instructing in Skyhawks, but a good $10,000+ in hull coverage might help save you some serious grief if you do some minor damage like bending a wingtip or hitting something with a prop requiring a tear-down inspection, or it may cover the deductible even if the damage is covered. Deductibles can be several thousand dollars even if other coverage does take effect.
Also, as a professional, please advise your aircraft-owner students to check with their insurance and find out what needs to happen to ensure they remain covered while receiving flight instruction in their airplane. This is not automatic.