I'm going to again ask for a more directly Jungian explanation from someone on this but as far as I understand it, Si wants reliable information the most, which is one reason why SJs seem so tied to personal experience and expert opinion to some people.
Both sensing function attitudes (Si and Se) use sense perceptions to gather information.
But Si doesn’t just take in information in the moment, like Se. It’s introverted, or inwardly directed. That means it captures the direct sensory experience and ruminates over it later. Which makes sense because what is more ‘reliable’ than a direct sensory experience that you get to spend time thinking about? A captured experience that can be reviewed later is a memory, the basis of this process.
That's why it gets mixed up with memory. Memory is a skill or talent (i.e. possessing a good memory). But Si is more linked to the actual noun, itself (a memory).
I believe @Kynx has given a better explanation of some of the subjectivity definition further up if you can think in Jungian language closer to the theory.
No, SI doesn't ruminate information later, it filters information in the present, according to whatever subjective structures one has in their psyche. This can give very peculiar results with the highly introverted person as they can perceive things very differently than others, or even perceive things that did not happen. I face this on the daily with my SI mother, she hears and see things very differently and has to take a while to observe something unknown to understand it's full shape and what it is. Superstition is also a common SI type trait, perhaps with some help from tapping into their bad N(I). Nostalgia seems more of a F thing to me, as it's basically something valued.
Also, as I've said before, SI isn't a function, which is important because you can put S and I on two different axes to represent one's inclinations. Same with the other function-attitudes.
I'm apprehensive about his idea on the collective unconscious being some inherited memory thing that introverts use to navigate the world (object). But I guess if our brains have the inclination to see things in specific abstracted ways for the sake of making prognoses, and introverts, because of their defensive stance engage it more, it could make some sense.
And yea, SI is one of those that are very misunderstood. Has nothing to do with making lists either, which is a judging process, or as Jung called it Ratio-nal. Judging is responsible in creating formulas, measuring, and whatnot.