Yeah that sudden brown change right after shocking almost always points to metals reacting, especially iron. I ran into this once after topping off with well water and it was pretty shocking to see because the pool was crystal clear before I added the shock.
What happens is the chlorine oxidizes the dissolved iron and it basically turns into tiny rust-colored particles in the water. Mine went from clear to a tea color in less than an hour. The filter will slowly catch some of it, but it can take a while depending on how fine the particles are.
One thing that helped in my case was watching the pH as well. When my pH drifted up around 7.8 the color looked even darker, but after bringing it closer to about 7.2 to 7.4 the water started clearing faster while the filter was running. My filter pressure even climbed about 4 psi that day because it was grabbing so much of that oxidized metal.
If it’s from fill water like you mentioned, it usually settles down once the system runs for a bit and the metals get handled. The first time it happens though it definitely makes you think something went seriously wrong.