Each outlet of the pair is fed 120V NOT 240V.
It is covered in other Articles, also.
This has actually been rather interesting. You can split the outlet and feed it
with two phases. This is called a multi-wire branch circuit and the conductors
feeding the split outlet must be on a 2 pole breaker. No jerryrigging is
involved.
What spooked me with the OP was he said when ever he turned either switch on
there is power at the outlet. It /sounded/ like someone was switching the
neutral OR the oulet was simply on a 3-way switch, any way it didn't sound
right.
I just got off the phone with my local (state) Inspector and to my amazement I
may no longer be licensed, that sucks because I hold/held a masters. I
originally called about the split outlet because I just could not find it in the
code book and he let me know about the new licensing schedules around here.
I know that the neutral was at one time called the identified conductor in the
code book but I couldn't find that either, odd.
WOW, this thread went a lot of places and I hope the original poster got his
answer.