Perhaps it helps to think of the actual D string. Your 6th is now an octave lower than that. So low E is on the 2nd fret, just like first-line E is on the 2nd fret of the 4th string. In other words, tuning is exactly "as written". So yep, position of notes is 2 frets higher. (Which is why it might help to think of your D or 4th string.) It's such a common tuning you'll get used to it very quickly!
2015 Connor spruce/Indian rosewood
1978 Ramirez 1a cedar