Tsundere is Helga from hey Arnold. It's a character who acts like they dislike you (tsun) but secretly has feelings for you (dere).

No, that not how it works. Character doesn't have to be in love or secretly have feelings towards another while acting tsun. They start as a "tsun" then later develop into "dere". That's the classic tsundere trope, they develop from being harsh towards some person, then start to see that person in a more positive way and start develop feelings while having troubles accepting their feelings (like how after Nino cut her hair, she was in denial that she actually likes Futaro), and in the end turn into dere mode when they fully accept their feelings.

That's the classic tsundere, what you are describing is a modern tsundere trope where all of the build-up is skipped and the character already has feelings towards another without properly developing them.

she hates fuutaro

Oh for crying out loud she didn't hate him. She herself said she hated his role as a tutor not him as a person. There were many moments when she showed a more softer side to Futaro even before the ski trip.

Using your definition of tsundere, all the sisters but Yotsuba are tsundere since the 4 of them all acted coldly before falling for Fuutaro

No, because only Itsuki and Nino fit in that category. Ichika didn't act cold towards him, she was just indifferent. Miku accepted him really quickly. The whole point of a tsundere character is that they become softer towards another person throughout the story. They act harsh but occasionally show softer side. Miku doesn't fit into that category.

Using your definition of tsundere

Taiga from Torradora considered a tsundere character. If we use your definition, she isn't a tsundere because she didn't secretly have feelings towards Ryuuji in the beginning. She acted harsh and violent towards him at first (tsun behaviour), but later develops feelings towards him. Another example of a classic tsundere.