I opened a jar of English mustard with a flat plastic lid and it didn't pop. It wasn't bulging or anything and contains citric acid. Is it supposed to pop? I notice French's mustard (North American style squeezable kind) doesn't pop so I think it's the same. It's just that we are so conditioned to expect jars to pop that when they don't I wonder. Mayonnaise doesn't either which I know is okay...
Plastic usually does not pop, it bends slowly under the pressure differential. Metal usually bends quickly and pops when the vacuum in a jar is relieved. Some jars use thicker metal that wont bend, so you have to listen for the rushing intake of air. Sometimes now they replace air with nitrogen before sealing. You won't get a pop or any other sound from a jar canned that way.
It can depend on the manufacturer, and on the lid. You may be associating the pop with metal lids, where you'll often see is a small circle in the middle of the lid, which is part of tamper-proofing. When the jar is sealed at the factory, it is sealed under pressure so that the circle is depressed. When you open the jar at home, the pressure equalizes, and the the circle will go back to normal, which is the pop that you hear. The tamper-proofing aspect is that you can be sure you're the only person to have opened that jar since the factory if it has one of the circles and pops when you open it. If you can press it in the supermarket so that it clicks in and out, the jar has already been opened.
However, as your jar had a plastic lid, it won't have that same protection. You're probably just accustomed to hearing the pops from metal lids.
Note: this is in the UK, I don't know where you live, or even if this technique is widespread.