what kind of "popping noise"?
When heated sauce is put into a jar and the lid is applied, when it cools it will create a vacuum. So even though you may not have done a boiling water bath, it's likely the jar created a vacuum that "popped" when opened. Even a room temp sauce put into the jar and refrigerated will create a vacuum because of the temp differences.
On the other hand....if it was a PFFFT kind of sound....which is what happens when something spoils and off-gasses building up pressure in the jar. Often times chile products will do a type of fermentation when they spoil, and not the good kind of fermentation for making sauces.
3Tbsp vinegar in about 1.5 cups of sauce is a little light, but considering it's been refrigerated, and if the POP was from breaking a vaccum on the lid, I'd go for safe.
Beyond this example, sauces can be good for 3 days (with no acidity in them) to infinity and beyond for things like Tabasco, Tapatio, and other sauces with really low pH..... the color may deteriorate over time, but the product should be safe to eat.