Restaurants have to be members of Dining Plus for you to get credit. No tie, specifically, to UAL Visa as any registered credit card will work with D+. I don't recal now whether it was an opt-in entry in my D+ profile, but I get an email for every qualifying meal that also summarizes the points and bonus earned.

Of course, every now and then you'll happen to eat in a D+ restaurant that you didn't know was a member and you'll get some unexpected mileage.