aseqjoy uses the ALSA sequencer API to emit the MIDI events. Therefore it creates an output port named after joystick used. You can then use for example aconnect (from alsa-utils) or Robert Ham's alsa-patch-bay to connect an aseqjoy instance to an input port of your choice.
Each axis of the joystick device is mapped to a specific MIDI controller. Moving the joystick along an axis will cause aseqjoy to emit MIDI controller messages via ALSA's sequencer API. The value of the controller message represents the joystick's position along the axis (eg 'left' -> 0, 'middle' -> 63, 'right' -> 127).