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Under 'Allies Of Convenience' of page 112 it says this...

This means that, for example, Allies of Convenience units:
. Can't benefit from the Warlord Trait of an allied character.
. Cannot be joined by allied Independent Characters.

As I understand it, my Tau Commander could not join an allied Chaos Lord, but the Chaos Lord could join the Tau commander or any Tau unit because the only restriction is of the Independent Character from the Primary Detachment of joining allies, not the other way round.

No.

You're confusing the name of the alliance with the Allied Detachment.

You have a Primary Detachment and an Allied Detachment. Those two detachments are Allies of Convenience. The rule forbidding characters from joining allied units works both ways.

I'm not seeing the distinction between primary and allied detachment.

Your linked reference seems to be imposing the limitation on both sides of the alliance.

Ah I see what you mean, oh well worth the try.

The "Allies" rules are independent of detachment, and apply equally to both. None of the rules on page 112 reference detachment at all, only the units and their relationship as defined by the matrix. So it is reflexive. the Chaos Lord can't join Tau units just as the Tau Commander can't join CSM units.