You cannot preserve just any salsa recipe (unless you're just freezing it).
Tomatoes are on the border between acidic and non-acidic foods. What this means is that they can be water-bath canned if they are sufficiently high in acid; but, if they are low in acid, they need to be pressure canned.
If you want to be sure to avoid trouble, follow a tested recipe. Salsa recipes will have a careful balance of low and high acid ingredients. Do not alter the proportion of acids (tomatoes and vinegar or lime/lemon juice) and low-acids (other vegetables, peppers, etc).
The recipe you choose should specify if it requires pressure canning or water-bath canning. One of those two methods must be used, though... you can't just put it in jars and save it.
For tested recipes, see the Ball Blue Book, the Ball website, or the National Center for Home Food Preservation.
In general, if jars are improperly processed or don't seal, you reprocess them exactly the same way you did the first time. This doesn't depend on the original recipe; you just have to do the exact same thing over again. In your case, since it sounds like your original process was hot pack, you would have to open the jars, dump out the salsa and reheat it, resterilize the jars, and reprocess.
But in your case, unfortunately, it's too late. If you didn't process it long enough the first time, you have to assume that it wasn't sterile, and treat it as equivalent to not canning it at all. Yes, probability-wise, your situation is safer than that, but you have to plan for the worst case, because you have no way to tell. Something may have grown in there. Canning just isn't a good place to mess around with safety.
And before someone chimes in and says it, yes, if you're the kind of person who eats things that have been left out way longer than is reliably safe, you could save it. It'll work out some fraction of the time, so there are plenty of people out there who can truthfully say "I've done this and never had a problem." But it could also get you sick, so I can't recommend it.
Best Answer
The key here is really how long it sits out at room temperature before you realize. The vinegar is acidic, so presumably it's part of bringing the pH to a safe one for boiling water canning. Without it, the salsa won't be safe to can like this.
If you realize right away and recan immediately, it's basically just cooking it extra. It may not be as good with the extra cooking, but it'll be safe. Similarly, if you immediately refrigerate then reheat, it spends a bit longer in the danger zone, but it should be easily within a safe margin.
On the other hand, if it sits out for hours, all bets are off. You made something not safe to store at room temperature, then stored it at room temperature, so you really can't know it's still safe.