The reason why you’re not getting the binaural effect is because some audio interfaces (like the SB K3+) and mixing consoles do not offer a panning feature for the individual channels. The 1 & 2 channel inputs are simply centered in both L&R outputs. This means you hear the left ear of the 3Dio in both the right and left headphones. Same for the right ear.
To get around this, you can monitor directly from your computer and use a DAW like Audacity, Garage Band, Cubase, Logic, Pro Tools, etc. to pan the channels left and right. With your headphones plugged into the computer’s headphone output, you can use the DAW to manipulate the audio to provide you with a true stereo (and binaural) mix.
One thing I should mention is that some DAWs may present a slight delay in the audio. You can usually fix this by adjusting the buffer speed of the audio processing. This setting is typically found in the ‘Preferences’ section of the DAW software. A quick Google search should render instructions on how to adjust this. It’s often called latency in the world of pro audio.