Re: am I responsible for this?
I initially read your question as asking whether you could get out of the judgment because it was rendered by a temporary judge. After reading Mr. Bravos's answer, I see that you were really asking about the substance of the judgment. I apologize for my misunderstanding.
After the accident, the other driver was entitled to recover the value of his vehicle based upon the condition it was in right before the accident. If he owed more than it was worth (as many drivers do), then the excess loan balance should not have been part of the judgment.
Let's say the car was worth $4,000 and the driver owed $7,000 on it. Before the accident he was upside down by $3,000. The judgment should have been for $4,000, minus whatever he had already recovered. That way he would still be upside down by $3,000 and would have been made whole. If the court awarded him $7,000 less what he had already recovered, then he would no longer be upside down at all and would have reaped a $3,000 windfall at your expense.
Looking at it another way, let's suppose I owned an identical $4,000 car that was totaled but that I didn't have a car loan. My loss would be identical to the plaintiff's, and it would take the same $4,000 (less the deductible) to make me whole. There is no good reason to give him $3,000 more than me for an identical loss. The only difference in our situations is that he owed $7,000 to a lender. But your actions did not cause him to owe that money, and it was unjust to make you pay it off for him.
What I said before about your insurance is still correct -- if the plaintiff signed a waiver when your insurance paid him, he should not be able to recover any money from you.
I agree with Mr. Bravos that you may still be able to appeal the judgment depending upon how long ago it was entered. A small claims appeal results in a new trial, where you will be able to use any waiver he may have signed as evidence against him. Contact your insurance company immediately to see if he signed one. If he did, to get a certified copy from the insurer.
Bear in mind that the parties are allowed to bring lawyers to small claims appeals. You don't have to do this, but you may want to anyway -- especially if you think your opponent is going to bring one.