If it didn't backfire before the tune-up, it is most likely a result of the tune-up. If your points are set incorrectly it will affect timing, advanced or retarded. If it is backfiring through the carb your timing may be too far advanced, if tailpipe too far retarded. Check that plug wires are not crossed. Did you get a good cap and rotor? ( I bought one from MACS and the rotor will move more than .100" on shaft, can't time that out) It could be any number of things but that's not how the smart money is betting.
1932 V8 had it right, please provide more info, type engine/ distributor, etc.