And having military outpost under no circumstance means jurisdiction, otherwise US would have jurisdiction over South Korea and Japan since there are numerous US military bases(outposts) in both East Asian countries.

My fellow Filipino friend, citing historical documents from the government of US, which is over ten thousands kilometers away from the South China Sea, is apparently not convincing. I'm talking about the CURRENT status of control, which is the fact that Ren'ai Reef is routinely patrolled by China Coast Guard and Philippine attempts to approach the Ren'ai Reef are being blocked by China Coast Guard ships.
Video of Philippine ships blocked by China:
https://www.youtube.com/watch?v=6AftQCuV9BE
https://www.youtube.com/watch?v=T-TyQ8noJtQ

https://www.globaltimes.cn/page/202308/1296738.shtml
"The China Coast Guard (CCG) on Sunday took restriction measures when Philippine vessels again trespassed into waters off a Chinese reef in the South China Sea"
No such thing as Philippine jurisdiction in Ren'ai Shoal

Nope, an academic article published in US Naval War College Review clearly state that coast guard patrolling can be
"defenders of sovereignty".
Source: https://digital-commons.usnwc.edu/cgi/viewcontent.cgi?article=1016&context=nwc-review