In fact, you have already analyzed the reason very clearly. You can sum it up in one sentence: the paint you choose is not specific for candles.
There are many kinds of pigments. If you choose the wrong flame retardant, you may not be able to burn it at all. Be sure to use candle-specific paint.
Color powder is what our industry calls color essence. This is flame retardant, but the advantage is that it does not fade. Generally, those who are superstitious about candles and use very thick bamboo sticks or reed poles as wicks use this. Craft candles with cotton wicks generally do not use this color essence.
As for the liquid ink you mentioned is not used in our industry, I have not used it so it is difficult to publish, but it is definitely not good if it cannot be burned.
No way, you have to choose the factory method. You have to find professional candle pigments online, buy them and then dilute them, dilute them with paraffin, and check the coloring ability of the pigments, for example, dilute it 10 times, and then When making candles, add it in a ratio of 1‰-1, depending on the color. Even if it is a special pigment for candles, it will still be flame retardant if the proportion is large. What you asked is quite professional and requires you to explore it yourself. It is difficult to explain clearly in just a few words.