The only two bases I can think of in NJ are McGuire AFB and Ft Dix.
McGuire is only an airlift base, AFAIK. I don't know what all Ft Dix has, but what you described sounds like artillery practice to me. You'd see the flashes of light pretty soon after they occurred (when the big guns were fired), but if they're shooting at a good distance away from your location, it would take much longer for you to be able to hear the rounds impact.
Having been around the artillery some, that's my best guess. They'd have to be lobbing those rounds a helluva long way for there to be a 10 minunte delay from when you saw the flashes to when you heard them impact.
My best advice is to keep your eye on the local news.