The music is notated as if there had been no detuning so that you can use the natural finger positions. (For example, a note that is notated as a C would actually sound as a B.) The trade-off is that it makes some of the intervals look wrong, but you do get used to it.
Bach's 5th cello suite also uses this technique where the A string is tuned down to a G. (The technical term is "scordatura.")
Interesting! On the guitar when alternate tunings are used, the pitches are written as they sound.
I wonder if maybe the difference is due to the fact that alternate fingerings are very common for guitar (because of having more strings spaced closer together). So notating pitches assuming a specific fingering doesn't make sense.
Plus I don't think the mapping from the staff to muscle memory for guitar is nearly as strong because we have frets.
Bach's 5th cello suite also uses this technique where the A string is tuned down to a G. (The technical term is "scordatura.")