There is no in-book discussion of this, so all we have is speculation. That being said,
is the most likely answer. The synthetic tribes require land upon which to place themselves, and the traditional states are presumably able to levy taxes upon blocks of land (e.g, "rent") without needing to "trace/follow people's financial activities." The setting of the majority of the book is called the "Leased Territories".
The geographical lines around authority are discussed in the book, e.g.:
His natural impulse had been to summon the police. But since they
were on the Causeway, this would mean the Shanghai Police again.
And the value of real estate:
MPS made consumer goods and ITL made real estate, which was, as ever,
where the real money was. Counted by the hectare, it didn't amount to
much - just a few strategically placed islands really, counties rather
than continents - but it was the most expensive real estate in the
world outside of a few blessed places like Tokyo, San Franciso, and
Which - to put in the context of the book - means that the ability to generate synthetic real estate, connected by causeway to but outside the traditional ownership of existing geopolitical states - was very valuable commodity.
China must be a signatory to the Common Economic Protocol:
"The CEP code," said the Sikh, "governs all kinds of economic
interactions between people and organizations.... As Protocol does not
aspire to sovereign status, we work in cooperation with the indigenous
justice system of CEP signatories in order to pursue such cases."
With crime, as we see in Bud's case, that interaction is a justice system. With the various tribes the interaction is that in return for money, the barbarians get land.
(Incidentally, I'm sure that CEP ensures that the Middle Kingdom will get some renumeration from the Ashanti tribe for having prosecuted Bud's case. If Bud had belonged to a tribe, they would have had to pony up some as well, under the CEP. I think Justice is a resource, just like Land.)
But as we see at the end of the book, the whole push of the Chinese has been to expel the barbarians from their land:
Then all of the barbarians stepped into the ocean, leaving their
filthy clothes strewn across the beach, relinquishing the last
foothold of Chinese soil to the Celestial Kingdom.... By the time the last girl's foot broke contact with the sandy ocean bottom, the end of the land had already been claimed by a man with a scarlet girdle round his waist, who stood on the shore laughing to think that now the Middle Kingdom was at last a whole country once more.
How well they'll manage to return to a traditional state - without the Seed to nurture their Confucian society, without the expertise in the Feed to compete at a high level - we never get to see.