I thought it was quite clear that Day came after Name, especially with Clara's access to new information and 11 referencing the War Doctor. What I'd much rather know is how Clara is able to retain the knowledge of her confetti self (such as remembering Gallifrey) when she is the original copy, so to speak. Kind of like how Rory remembered his 2000 years as an auton when that was reset, something which I never really got either.
I don't think it matters too much as to how they got out, it's probably left up to the viewer's imagination. In my mind, the Doctor knew that as it was his timeline, he couldn't get chopped up into confetti. But he thought Clara was dead, until the psychic link with River confirmed otherwise. Then, it was just a case of going in to retrieve her.
I thought that in the special he would come across Ten by exiting the timeline at the wrong place. Using this theory that he can exit the timeline in this way, he probably just found the point at which he entered it so then he could carry on his own timeline as normal.