I’ve seen those reports, and I’ve tried to reconcile them with temperature data from Greenland ice cores. Although there is a drop in temperature at the point of increased sulfur deposits from Toba, the temp graph of the last ice age looks very similar to the temp graph of the one just before that. Perhaps the drop in temperature and rebound to the “normal” rate of change was so rapid that it doesn’t show up well in the ice cores. A volcanic winter lasting a few centuries, or even just a few decades, might have been long enough to create the human bottleneck, but not long enough to have altered the general climate trend nor have shown up in the core samples.
The climate guesstimates I heard were all based on O16-O18 ratio in microfauna from sea floor sediments.
How well that correlates to other data we will never be sure, but the truth is probably somewhere in the middle.
Toba was a monster event.
http://volcano.und.edu/vwdocs/volc_images/southeast_asia/indonesia/toba.html