What triggers the trim horn and the "stabilizer motion" aural callout on the MD80?
There are two aural sounds, the horn, and the voice callout "stabilizer motion".


The horn sounds every 0.5° of trim change after the initial 0.5–1°.
"Stabilizer motion" sounds when the autopilot or runaway trim motor make a >2° in 30 seconds.


So your second source is the correct one. See text below from an MD-80 flight manual:


  Momentary horn sound starts after 0.5º to 1.0º of stabilizer movement and repeats every 0.5º of stabilizer movement . "STABILIZER MOTION" voice warnings will sound when either the autopilot or a runaway trim motor moves the stabilizer more than 2º in 30 seconds and will continue to sound as long as stabilizer moves. Cycle continues until stabilizer movement ceases. (Manual page)


Note that it also says:


  Vocal warning on some aircraft, other aircraft no vocal warning.


So not all MD-80s have the voice saying "stabilizer motion".