Do I need a US visa if I get a connecting flight at Seattle-Tacoma International to Vancouver?

I am flying from Keflavík, Iceland to Vancouver and have a flight change at Seattle. I am going to Canada with a work permit (from the UK) and so will be staying there for up to 12 months. Will I go through US customs at Seattle to get the connecting flight? And if so does anyone know if I need to satisfy the US... show more I am flying from Keflavík, Iceland to Vancouver and have a flight change at Seattle. I am going to Canada with a work permit (from the UK) and so will be staying there for up to 12 months. Will I go through US customs at Seattle to get the connecting flight? And if so does anyone know if I need to satisfy the US visa waiver conditions that I show proof that I will be leaving north america within 90 days of my arrival? Thanks.
Update: I did a bit more checking after all the excellent and prompt answers I received: Because I have a work permit to be in Canada for up to 12 months and that I have a connecting flight (my layover at Seattle is only 4 hours) then I will satisfy the US customs on arrival under the VWP and should not have any... show more I did a bit more checking after all the excellent and prompt answers I received:

Because I have a work permit to be in Canada for up to 12 months and that I have a connecting flight (my layover at Seattle is only 4 hours) then I will satisfy the US customs on arrival under the VWP and should not have any problems. The only clause of the VWP I will be breaking is that I will be in North America for more than 90 days, but my work permit will sort that unless I have a particularly grumpy customs official! Thanks for all your answers.
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