What does it mean when a jar lid pops

The seal, the pot, none of it really matters.

You don't sterilize food when you cook it, you pasteurize.

Even if it was perfectly sealed, there's still baddies that didn't get killed. Pasteurization brings food bateria to a safe level, not a 0 level. Once food gets back in the 'danger zone', it can start growing pretty quick again.

This is the same reason you can't cook a sous vide meal and then leave it on the counter forever.

It is likely that prior to use there is minimal likelihood of the ingredients separating as the transport and shelf storage of the item is likely considered controlled. Once in a home kitchen, the problem is not with spoilage (there are plenty of preservatives in it), but that storage fluctuations and use may throw the emulsifiers.

Although I am inclined to dismiss the need for refrigerating it, the is likely that across a few million units, a less stable batch may make its way into a hot and then cold and hot and then cold kitchen and the contents would separate.

For big brands, a major focus is to ensure consistency among products in spite of quality or diverse ingredients; hence watery domestic beer (U.S.), Lay's potato chips, and refrigerated chocolate syrup that is harder to use than when stored at room temp.