While not as unique as fingerprints, individual magmatic systems tend to have somewhat individualized geochemical profiles in terms of concentrations of trace elements and isotopic ratios so it's not "guessing" to use similarities of geochemistry to argue that two adjacent volcanoes share a source and/or have intermingling of sources in the shallow crust. Additionally, there are variety of geophysical techniques (seismic tomography, magnetotellurics, resistivity, etc) that allow us to image the magmatic systems of volcanoes which again provide evidence that these are related. The general idea that geology is all "educated guessing" (which underlies many questions and lay answers/comments in this subreddit) is pretty frustrating given the extreme care and detailed analysis many of us put into to understanding the details of natural systems.

On a slightly smaller scale we've sismic imagery (think like a sonogram) of a lot of the near surface plumbing on the big island so that cover Kilauea, Manua Loa, and a few other features. If you read about the 2018 eruption of Kilauea you'll see that in action as it's all about a loss of pressure in the system.

I'd also add that the hotspot didn't just make the modern Hawaiian Islands. There's a whole chain of eroded sea mounts that used to be other islands! And the direction they go in is in the direction the Pacific plates is moving. And this is a trait we see in other hot spit volcanos. Since the souce of the heat is from the mantle it doesn't move, but the plates still move over it.