The DX-EE is a parallel dipole antenna, similar to a fan dipole. It has a wire tuned for each band. However, the "top" wire combines 20 and 40 meters. Any adjustments you make to the 20m band (the first leg of this top wire before the coil) will also affect performance on 40m. The coil acts like a trap at 20m and as a loading coil for 40m, since the physical length is shortened.
When tuning, start with the 20m section. Then, move to the 40m section. Adjust the 40m wire (coil to insulator) as necessary. Then, move to the next wires in order. For more information, please see the Alpha Delta Multi-Band Dipoles Instructions.
Notes
According to the designer of this antenna, you don't need cut the wires to tune. For short adjustments, wrap the excess length back over the main wire.