In the 12th century medieval knights normally wore plain metallic chainmail coats or rudimentary armours, rather than the kind of full body plate armours that we might see exposed in castles (those only really came at the end of the Middle Age and in the Renaissance, the same time the illustration of the article you linked was painted).

The knights' colours and distinctive signs (literally their coat of arms) were represented not on the armour itself but on a generally sleeveless coat (named tabard) that they wore over the chainmail. In the context of the Crusades, the Templars' white tabard with a red cross is quite well-known, for instance.

Heraldry is the discipline which sets the rules for those distinctive signs. Some symbols like lions or eagles are quite established, and colours may have deep significance for those who adopted them, but there has never been any clear, universal significance of a particular symbol or colour. The person who adopted the coat of arms certainly thought about a meaning but it is hardly possible to deduce it in reverse.

So what about plain green arms? Green has been associated with lots of different meanings so once again it would be very speculative to claim we know what Sancho Martin wanted to express. What is relevant, though, isn't the colour but the way the knight is called: "the Green Knight", as if his arms were just plain green. This is completely in line with medieval literature (particularly in the Arthurian stories), where some particularly important/strong/etc. knights use plain colours and are referred as "the Black Knight", "the Red Knight", etc. A big principle in heraldry is that your coat of arms has to be absolutely unique. And there are only a handful of colours one can use. So of course bearing a plain one-colour coat of arms is an honour that only a very few people in all history could have boasted about. That's why it was used so much in fiction, and that's also why I think we can doubt that Sancho Martin's arms were plain green, and suspect it was added or exagerated by the chroniclers to make him look even more of an ideal knight.

The high middle ages is before my period of specialization, so I cannot speak to the Siege of Tyre speicifically and what sort of painted armour may have existed in the period.

First off, it is important to talk about survival bias. Very little medieval armour survives, and even when it does it has been cleaned, 'restored' and altered for hundreds of years before we see it. In some cases painted armour has had its paint polished off, and in others paint has been added later. The other forms of evidence we have for armour (accounts and artwork) have their own problems - art may show things according to convention, or for aesthetic reasons, and not show what something looked like in person. Accounts may just not mention details like painting. With that being said, here is what we can piece together about painted armour:

I will continue by quoting my earlier response on armour surfaces in the later middle ages, and why it was done:

Some economic background. The majority of labour in plate armour is the polishing - something like 80% of the man hours to make a full harness is spent polishing it. Armour is in general very labor intensive, and unlike many other medieval goods (clothes) the cost of armour is largely the cost of labor, not the cost of materials (materials make up less than 10% of armour's cost by the 16th century). So much of the savings that a finish can provide is not the maintenance benefit, but the front-end benefit of avoiding polishing or allowing less intensive polishing. However, paint is a method of finish and decoration that can be applied to unpolished armour. It protects the metal, provides decoration and negates the need for polishing. Alternately, some armours appear to have been completed with the scale from forging still on, forming a black finish.

Some sallets and proto-close helms of the late 15th and early 16th centuries are decorated with paint. The 15th century sallets are commonly called 'black sallets' because they are unpolished. A number of the early 16th century ones are painted with grotesque monsters on the face. These helmets seem to have mostly been worn by medium cavalry that rode mostly unarmoured horses and wore armour without sabbatons or greaves - a famous portrait of this kind of horseman is Durer's The Knight the Devil and Death. At the very least, painted helmets provided decoration that was affordable to men who were at the bottom of the aristocratic economic ladder. In some cases the decoration appears to have identified units of cavalrymen - a certain unit of Nurnbergers might wear monster faces on their helmets to identify themselves as part of the same unit, for instance.

An example of this painting can be seen at the Bayerisches Nationalmuseum in Munich. Some other sallets are painted with geometrical designs in colors that may be heraldric or signifying membership in a particular retinue, for instance this sallet from Ulm, now in Vienna.

Looking earlier, a bit later than the Siege of Tyre, some of the helmets in the Maciejowski Bible are brightly painted - in this case red. However it is hard to tell when this reflects practice and when artists are doing it for effect, and only a handful of 13th century helmets survive, none with paint.

The main surviving painted body armour we have is the mid 16th century 'black and white armour' from the Holy Roman Empire, which is post-medieval.

Sources:

Tobias Capwell - Masterpieces of Armour at the Wallace Collection (notes on painted sallets)

Claude Blair - European Armour 1066-1700

Alan Williams - The Knight and the Blast Furnace - Notes on the relative labor involved in armour-making and the sources of armour's cost