Both your tie class and the overloaded add are not quite correct.

The FETCH routine does not return a scalar of the expected kind. You have it returning a reference to the underlying hash, rather than some scalar data stored in it.

An overridden operator like '+' is written like a constructor. It should take data from its arguments and return a new object of the correct type constructed from the result. What you have written for add is a mutator which behaves more like '.=' than '+'. It is a good idea to make sure overridden operators are as much like the builtins as possible.

I'm not sure there is a way to make a tied variable honor the underlying classes' operator overrides. I wasn't aware of that, but my attempts to make it happen have failed.