this is to some extent a difficult question to answer - while there are well-documented Maya disruptions in the middle of the 6th century, they seem to be concentrated in the period immediately following 540 CE, therefore a few years after the 536 eruption and initial misery documented in the Mediterranean. Recent research by Dull et al. 2019 suggest that the reason for this is the TBJ eruption of Ilpango, the second of the so-called "double eruption" that caused multi-decadal climate anomalies in Eurasia.

The consequences for this, on a cultural level, are of course severe. Ilpango is in modern El Salvador, one of the most densely populated areas of Mesamerica in the 6th century, and the region was utterly devastated by the eruption (one of the 10 largest in human history). Dull estimates 100,000 fatalities due to the eruption, which caused massive population collapse. Analysis at Quelepa indicates a disruption in the 6th century, coinciding with the boundary between Shila and Lepa - while the initial report of the site discusses it as an absence to volcanic influence, it was thought before 2001 that this particular eruption occurred in the 2nd century AD.

However, this new dating hasn't yet been contextualized by the broader archaeological and cultural historical community for mesoamerica, as far as I am aware, so while I can provide the volcanological information, i certainly welcome comments from people more familiar with the relevant period in Maya culture to more broadly contextualize the cultural shift in the period.