She is a tsundere. You don't have to be outspoken to be tsundere. Eriko from Kimikiss also is considered to be tsundere though she is far from being outspoken or loud. She just treats the main character both harsh (tsun) and sweet (dere). It's enough for you to act both dere and tsun to be a tsundere...
However it is also needed that both tsun and dere would be part of the same relationship (with the same person(s)). Since Taiga for majority of time was treating Ryuuji badly (tsun) without giving any dere moments to him she wasn't a real tsundere up to this point. Yet with episode 8 she can be considered a full-blown tsundere.
But because of later popularity of the term now tsundere definition became so wide so that now almost any stronger female character can fall into this definition.
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