You’re right.

Adding "que ça" doesn’t add meaning to the sentence.

It just adds a bit of emphasis or a comparison to the situation.

In Joseph est pas si timbré que ça, the adverb si is a comparative and might be replaced by aussi without introducing a significant nuance.

The sentence might then have read:

Joseph (n’)est pas aussi timbré que ça.

with aussi … que ça that can be interpreted to something like:

Joseph (n’)est pas aussi timbré qu’il n’y paraît or …qu’il n’en a l’air or …qu’on le dit.

i.e.:

Joseph is not as nutty as he looks/seems / not as nutty as people say.

Not sure about the idiomatic degree of "Joseph is not as nutty as that" in English but what is sure is that "Joseph is not as nutty" alone wouldn’t work.

This is not the case in French so the last part (que ça) can be removed because it doesn’t refer to anything :

Joseph (n’)est pas si timbré. → Joseph is not that nutty.

In conclusion, instead of considering que ça was added for emphasis, I’d rather say que ça is the second part of the comparison but refers to something so vague it can be removed for failing to add any piece of useful information.

When the second part of the comparison is elided, the role of si moves from comparative to intensive. Another intensive adverb that can be used here is tellement:

Joseph (n’)est pas tellement timbré.

You might have a look to this document for a deep analysis of the role of the intensive si :

La genèse discursive de l’intensité : le cas du si « intensif », CHR Plantin, Université Libre de Bruxelles, 1985.