There are numerous reasons for the attributions of colour and metal to the planets.
All function follows form and magicians were first and foremost, keen observers into nature and not just those who sought to manipulate it. Consequently, a lot of the attributions are empirically based (that is experimentally, rather than theoretically). So sometimes things do not seem to mesh very well and it can be confusing why certain attributions were chosen if we haven’t had the same experiences - and indeed, sometimes there are disagreements.
Since the function of an item is encoded in its form, then it was/is decided that we can use form to figure out function. i.e. if one item is similar to another then it may (likely) serve a similar purpose.
Following this, the basis of the attribution of the demons is to the planets (I don’t personally think they should be attributed to the planets perse but that is just me). So why these colours and these metals to these planets?
The first and simplest is…simple observation in the sky (remember, form defines function and their colour is part of their form and thus function). Some of these are unanimous and others not (as far as my knowledge).
Mars was always the red planet, the sun was naturally always yellow, Saturn is mostly black (it is a very dim “star” compared to the others). Then things get more difficult…stars (including the planets) are pretty much all white appearing, afterall. They’ve all been given numerous colours by many (spell-check keeps telling me I’m spelling colour wrong, slightly irksome). Jupiter being called Mul Babbar in Sumeria meaning “white star”…as it is a beautiful bright white when seen in the sky. This actually is an alternative colour that fits quite well for Jupiter compared to blue, I’m actually not certain from what blue might have initially originated. Venus happens to have what is called the Ashen light, a green glow sometimes seen on the nightside of it. This was only discovered in the 17th century (supposedly)…but personally I have no issue with a bit of alternative history where the ancients were aware of such too. Mercury often appears orange if you look at it in the morning with the sun. This leaves the moon…which hasn’t been violet whenever I’ve looked at it. Pesky little thing ruining everything (for this colour key anyhow).
But not to worry, there are other areas we can look at. Remember, magicians believed in certain fundamental powers which penetrated and operated everywhere (elements, planets etc) thus we are not limited in our search. Let us say we note that the pure white light (God) is refracted into 7 colours as found in the rainbow, representing the 7 basic planetary powers. We can already match most of the planets, we’re left with blue, violet and indigo. Indigo is the darkest and as there is no black, we decide it must belong to Saturn. Blue is the colour of the sky, the sky god Zeus, so it is natural we might attribute that to Jupiter. That just leaves the moon with violet.
A further derivation of these same colours can to a large extent be obtained through ideas of colour theory, hot and cold colours and how these apply to the natures of the planets. That is, Mars is described as hot and dry etc. Where those natures of the planets came from - astrological observations of the effects of these planets on the weather and from a medical viewpoint (based on the traditional ideas of the four humors of the body in greek and medieval medicine practices).
The fun doesn’t stop there though, on to the metals…which with our colour decisions are really much simpler. Gold does not tarnish, it is always gold. Equals yellow, equates to the sun. I have an old copper candlestick holder and it is oxidized to a beautiful green. Copper = green = venus. Tarnished silver turns black, now were you to rub it off with your hand you may note black and violet stains on your hand. Moon = violet = silver (though otherwise, silver is unanimously associated with the moon anyhow). Tin happens to oxidize to a blue-black colour (sometimes red) initially and then when fully oxidized to a white. So there we have both our blue and white. Mercury oxide is an orange colour again (and there is an important relationship to Antimony as well). I’m sure we’ve all seen the rust of iron for Mars (and of course iron was used for weapons). Lead also “conveniently” oxidizes to a black colour. Well golly gee.
Unfortunately, I have never looked into the associations of each of these as concerns the hierarchy of the lesser key, nor much physics of it (my training was in chemistry thus you just get oxidation of metals I’m afraid). So I can’t help you with the associations to the actual demons, sorry. I would start with getting a good understanding of the typical roles of dukes, marquis, earls etc in medieval Europe and meditate on that and the possible links. I’m sure some breadcrumbs to follow will come up (and don’t disparage yourself that such is out of your realm of thought - it need not be, particularly if you’re curious that is good enough ) Probably for the best I never looked into it since this has become a monster post…I’d be surprised if it’s even read.