This is the third different japanese media I see “True Ancestors” being used related to Vampires. Is it something to their culture to use that terminology?
Have you read anything like Rosario+Vampire before? (I do recommend that one for part 2's action scenes, they're
awesome)
True Ancestors, known as Shinso (in Japanese media), are a concept first popularized (AFAIK) in the original Dracula literature - i.e. the older the vampire, the stronger they are. The ideas behind this vary, but usually it's because they're the closest to whatever power originally spawned them, and are thus the ones holding the largest portion of might in their race. Later, lower-tier vampires are of "diluted blood" or whatever other explanation a specific piece of media uses, and thus have far more restricted, or complete absence of, vampiric powers.
A good example of this is that a lot of lower-tier vampires in media will have regenerative capabilities, but a Shinso will have such incredible durability and regeneration that they could literally be diced into thousands of pieces and regenerate from that.