Isn't it generally a backfire out the carb meaning lean, and a backfire out the tailpipe being rich? If it happens when you turn it off I'm guessing it's out the rear because you'd have the engine pushing some unburned fuel out after you cut off the spark. It's possible some of the seals/gaskets in the carb have degraded and allowed some gas to seep or flow through as it shouldn't. Could be as simple as some gunk holding something in the carb open, too. Try a bit of carb cleaner, see if it helps, if not perhaps rebuild the carb. If that doesn't fix the issue, well you've got a fresh carb that should provide better service once you've fixed the issue, so there's no loss. Alternately take it by a mechanic who knows older cars, and I'd be willing to bet he could tell you exactly what the problem is and have a simple fix for it. Hard for us to say without first hand experience what's going on.