For Dragonbloods, I know the ones that it states in the book outright, that airbloods can have blue skin white hair, firebloods can breathe smoke, waterbloods smell like the sea, etc. when they get old or have high breeding.

But what about the tattoo like ones that are mentioned in Dreams of the First Age, Lords of Creation (p 155 and p 159), there really isn't anything that states outright the rhyme or reason for them, but a couple of the Dragonblood sample characters have them described. Tried to find more information on it but apart from it being mentioned a couple times in fiction people write, and there only in passing, I haven't been able to find anything on it. Do they differ in different aspects? Do they only appear on certain parts of the body? Are they supposed to be certain colors?

This is pure guesswork but I'ma say Rule of Cool.

If your character would look cooler with tattoo-shaped elemental markings? Awesome!

If you mean the mandala's that are on Anjei Marama, it isn't that she had tattoos bred onto her, it's that she was specifically scarified in tattoo like ways, with the scarification designed to enhance her various assets, including her aspect markings. They were specifically added after her exaltation at age 8.

Yeah, but it did sound like her aspect markings appeared like tattoos, or some type of pattern since if she just had the change in skin color that is featured in the dragonblooded book it probably wouldn't be enhanced by scars since it's basically uniform all over her, then Chuzei Vagyan Zu is said to have "Well defined aspect features tracing blue whorls over his joints and chakras." (p 159 DotFA:Lords of Creation)

I know in Marama's case they are just tattoo's to enhance her aspect markings

There are those, but it's the aspect markings that are being enhanced that I'm interested in, and they're scar tatts, not inked tatts, and looking at the picture of her there's a lot more markings than can be accounted for that, since it's not in color I"m assuming that the white is the scar tatts while the darker markings might be the aspect markings they are supposed to emphasize. They certainly do hug and frame them.