I remember in Fallout 2 how i encountered SF. When i found them, they became one of my 3rd favorite faction(Enclave 2nd and House 1st). Question is though how did they become a part of NCR when they were advanced during there time. I posting this from the wiki.

"Technological level

The Shi are one of the most advanced factions in the wastes, surpassing even the Brotherhood of Steel. They have considerable industrial capability, being able to manufacture high tech weapons, both to equip their military force, and for trade. Perhaps their most awe-inspiring feat is the ability to restore pre-War T-51b power armor to working condition and offer them for sale.

The Shi are also very active researchers. They are nearing a breakthrough in the rediscovery of nuclear power and are considering methods of space travel. They have also learned to synthesize a new fuel using plant extracts and sea life. Since integrating pre-existing pipelines to their fuel reservoirs, they can direct fuel to a number of diverse areas, including the PMV Valdez. New weapons research and insights into new polymeric combat armor, with enhanced heat and penetration resistance, look like promising additions to the Shi armament, particularly when viewed in context with their construction capabilities. It is forecast that, with vertibird schematics, a prototype could be manufactured in a year. In an additional year, mass vertibird production would be viable.

Other, less militaristic, advances include radiation-resistant plant life in the Shi botany department, which is led by Dr. Sheng. Initial experimentation yielded results with unpleasant side effects, so it was posited that research be redirected to more critical areas. After Dr. Long Wang's experimentation of injecting himself with a FEV-derived serum to manufacture super soldiers failed, his genetic research department was merged with Dr. Sheng's botany department. Due to this merging, research on radiation-resistant plant life was resumed. The research culminated in a radiation consuming vine that scoured the San Francisco area of radiation after the Enclave's destruction".

Soooo anyway, there as pretty advanced as the BOS, on par with Vault City and the Enclave. I would think that they would start expanding to gain territory and eventually encounter NCR but who knows?

We still don't know if they became their own Empire. We don't even know if they are apart of NCR but it does seem like it. Colonel James Hsu is from San Fransisco.

My guess is that, they are peaceful and NCR made them a really great deal. Giving San Francisco Statehood within NCR. NCR was already very large and powerful by the time of Fallout 2. NCR takes over all of California, and the Shi become an Island. NCR became to powerful for the Shi to fight and NCR surrounds them. Can beat them might as well join them.