I see the faces of each quadra superimposed on a thematic background...
Alpha: bright, expectant, open faces. Holding hands. Superimposed on a world without any shadows and lots of distracting lights and sounds, like being in a video arcade.
Beta: changing expressions, sometimes the eyes are slits and other times they're open wide and fierce. For every action there's an opposite reaction, sometimes embracing and sometimes pushing others away. The background shifts and swirls a lot
Gamma: wry faces, they've seen it all and aren't impressed. Sad, often. Kind of a Blade Runner feeling world, dark and industrial, but hard to describe. The Ni worlds are less clear in form than the Si worlds.
Delta: faces turned away or eyes downcast/looking off in the distance. Stoic, lips in a thin straight line. A scene of a little cabin in the mountains in winter with smoke coming from the chimney. Everyone is holding a cup of tea and wearing wool mittens.
To your original question, OP: I don't have Si the way you do, but when I play the piano there are certain sounds that have a "color" to me. I think this is probably different than having such a strong and overwhelming presence of a color flooding your consciousness.