Tandem breaker needs both thrown to break circuit. Incorrectly wired?
Intentionally wiring the two breakers together in the breaker box would be a really stupid (borderline malicious) thing to do.

My guess is that there are supposed to be two independent circuits, but someone has somehow unintentionally joined them together in a junction box or outlet box somewhere along the circuit.

This could be pretty complex. I would recommend having an electrician come check out the situation.

If I were solving this, here is what I would do:


Work carefully! It's a dangerous situation when you can't be sure the power is off. Assume every box you encounter is live. You'll want a contact-less voltage sensor. 
Open the breaker box and verify that there are two 12/2 cables entering, the black wire of each connected directly to one lug on the tandem breaker.
Start drawing a diagram, including every switch and outlet involved.
Turn off both breakers.
Open a box that's affected, and disconnect the black wires from the device. Cap off the wires. I would start with the box that you think would be closest to the breaker box and first on the circuit.
Turn a breaker on, one at a time, and note which wires/devices still have power. This will help you figure out which wire heads upstream / downstream. Label the wires with numbers or descriptions (if you can write small enough) e.g. "From hall switch"
Repeat until you have the situation mapped out.
Report back here to tell the curious people what you found.