For questions on early man, it would be worth x-posting to our sister sub, /r/AskAnthropology. There are a few anthropologists here, so this sub is fine too, but you'll get more eyes on it over there.

In order to better answer this question, I'll have to cast a bigger net than just Indonesia and look toward India which was downwind from the eruption. I hope you don't mind.

According to Petraglia et al (2007) at the site of Jwalapuram in southern India, the 2.55m ash layer uncovered by mining activites is associated with the Youngest Toba Tuff of 74,000 years ago. They compared the glass shards from the tephra found to signatures of the Older, Middle, and Younger Toba Tuff and it came back as a match to the YTT. In several trenches placed in the area Petraglia et al found 215 stone tool artifacts found beneath the YTT layer. These tools are a typical style for the Indian Middle Paleolithic. Within the YTT ash layer they found 108 artifacts and above the ash layer 168 artifacts. While the ratios of material types are different in the post-Toba eruption, the types and style of artifacts still resemble other Middle Paleolithic tools indicating a continuity before, during, and after the Toba eruption in southern India. A more detailed explanation of the findings can be found in Haslam et al 2010.

As an aside, the tool types found at Jwalapuram resemble the African Middle Stone Age more than the contemporaneous Eurasian Middle Paleolithic. This would make sense considering the models of a southern dispersal of modern humans from the Horn of Africa.

Now Ambrose (1998) and Rampino and Ambrose (2000) try to attribute the genetic structure of ancient human populations to a sudden decline due to a cataclysmic event such as the Toba eruption. What Ambrose and Rampino don't consider is the founder effect on what happens when populations split off and move. While Henn et al (2012) don't discuss the effect from the Toba eruption directly, they do discuss the time period between 40kya and 65kyn in which one sees a "genetic bottleneck" brought on by fissioning groups which lowers the diversity of available genetic material. One could hypothesize then that paleoindians being the last wave of humans to settle previously unpopulated lands would have the lowest genetic diversity since they are the furthest away from the point of origin. And in fact, Native Americans do show some of the lowest amounts of diversity excluding possible subsequent migration waves into the Americas.