I'm thinking of two possibilities:
1) Red algae of some sort.
2) Iron leakage from the root tabs. I do not know what the API root tabs have in them, but it is likely that they contain iron as it is an essential nutrient for plants.
I highly doubt that either of your rocks are to blame. Neither of them look particularly iron rich. Additionally, if they are iron rich and oxidizing, the first place the red spots would appear would be on the surface of the rocks. After the oxidization appeared on the surface, any flaking off iron would probably be localized around the rocks rather than spread seemingly randomly throughout the tank.
Something that concerns me regarding your rocks though; they are both fossiliferous, meaning, containing fossils. Fossils of bivalves (clam like creatures) and gastropods (snail like creatures) are commonly found in rocks from a marine source. Most shells of bivalves and gastropods are constructed out of calcium carbonate. While the host-rocks themselves do not appear to be calcitic, the calcium carbonate in the fossils may increase the hardness of the water in your tank. I would suggest removing the rocks and testing them using vinegar. If they fizz, they will affect your hardness. If your intent is to have a higher KH in your tank, then leave them in.