Confusion about reserving Shinkansen tickets online and linking to IC card

Visiting Japan for the first time next week, I want to order Shinkansen tickets ahead of time for a round trip from Tokyo to Nagano on the JR East site. It says "Each passenger needs to have an IC card before boarding the train."

I have been trying to read about this stuff and I'm still a little confused how it works. But it sounds like you can link your tickets to the card after the fact, and the card is then your ticket? Do I have that correct?