It will depend on state liability laws if your son's actions could affect your own personal liability. If your adult son is still claimed as a dependant on your taxes then in some states you can still be held accountable for negligent actions which he might take part in.
With him having his own insurance policy on his own vehicle in general he should be held responsible for his actions in this vehicle. You as a parent have not provided him with the vehicle so he should be held responsible for an accident he is at-fault in. Again state laws will be the guide for this so you will want to check with a lawyer familiar with your state and local liability laws to find out for certain what you could be held responsible for in regards to your 18 year old live at home son.
If you find out that you can be held responsible for your son's actions, even though he is now an adult, you may want to see about obtaining an Umbrella policy. This type of policy can help you protect your assets.
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If you or your son are in need of an affordable car insurance policy, start getting auto insurance quotes here with us.