I don't believe you need to select a character. Just logging in should be sufficient, since at this point, you're using the ZoS account you created.
This event has run before.
I have always logged in and sometimes I log out and sometimes I get kicked for inactivity. I have received all crates in the previous event.
That was in reference when it came to logging in.A bit confusing but here's what they said in in the news; quote from link "logging out just to the character select screen will not work."