sangyey wrote:Does Samantabhadra belong to the Tataghata family?
I think I see where you're headed with this -- does the color indicate the Buddha family?
I don't think it really works like that. The Buddhas appear in many forms.
For example, Vajrasattva is usually white. But in the White Umbrella practice, Vajrasattva appears in his blue form. Khenpo Palden Sherab back in 1986 said that it's like our ordinary minds to work very hard at making distinctions.
However, I do not presume to understand the potential scope of your question. A think a good teacher can explain a great deal.
A good person to ask about colors is Lama Padma Karma Rinpoche. He does a lot with Buddha family colors and is adept at this topic: http://www.dzogchenstudies.com/teachers.html
The contact page is here: http://www.dzogchenstudies.com/Contact.html