If I understand correctly the stones turned red only after they had been left in the sun for a while. When you do this kind of scientific experiments you always have to have a sample to compare with. Otherwise you will not know for sure whether the reaction was because of what you did, or something else. To find out I took an old stone from the refrigerator and left it in the sun for a while. I had not used any sort of colouring agent. After a while it turned dark red-brownish on the outside. When it had melted the remains was red-brownish. Not as bright red as yours however. It could be a chemical reaction with the bile and oxygen catalysed by the sun. The bile consists of composition of bile salts, cholesterol and pigments. How the pigments react to the heat and sunlight could perhaps vary between gallstones. More experiments have to be made before we know for sure.
Inside the liver and intestines there is very little oxygen. I guess that is why the stones don’t start melting before they come out. Even when my stones have remained in the intestines for days due to constipation, they have not started to melt when they come out. But as soon as they come out, they always start to melt.
I don’t claim they really are gallstones, merely that your experiment isn’t proof that they are not. Personally I have been sceptical to the idea that they really are Gallstones from the beginning. But as long as I have no better idea I won’t dispute it. I’m still searching for the answer.