Does Jax's Counter Strike skill protect teammates behind him from Twitch's ultimate, or does the dodge only apply to himself?
No, Jax's Counter Strike dodge only applies on himself. Teammates behind him take full damage when they are hit by Twitch's ultimate.
You can see this in the following image (taken from Rift Myths on youtube)
(Keep in mind that Twitch's ultimate is changing and the answer to this question might change or become irrelevant.)