The appearance of red eyed pigmented birds is explained by the "ino" factor and can be used to described pigmented birds with red eyes in lipochrome mutations (red ino, white ino, yellow ino, etc).
So a yellow lipochrome is called a Lutino, while a red one is called a Rubino.
BECAUSE the ino factor belongs also to pigmented groups it doesn't mean it's related at all to the albino factor.