First, as explained earlier, the language and customs of enemies are not totally new to Mongols. Second, if you referring to engineers specifically, then it was the Jin (Chinese) dynasty that they learnt siege-craft from. The battles with Jin dynasty had many, many defections (Chinese to Mongol) of senior officials. So, it would have been straightforward after that for Mongols to identify these Chinese engineers. In fact, in the very first battle against the Jin dynasty, at Yehuling, the Chinese emissary defected! Clearly, their reputation preceded them.
Finally, and this is only for context, they did not always kill off everyone in the bigger towns/cities because they needed the population for trade and taxes. As you read in the Mongolian military tactics, their army was in fact extremely disciplined (their reputation notwithstanding). Hence, the Chinese engineers could still volunteer or join up with the Mongols after the dust has settled.
On sources, for Yehuling, the defection is stated in the Wikipedia article. On not killing off everyone, the sources are in almost all recent historical research. For instance, this is from chapter 4 - 'The rule of the infidels: the Mongols and the Islamic world', 'New Cambridge History of Islam' (Cambridge University Press, 2010), first paragraph:
"The Mongol period was a watershed for the Islamic world, as it was for most of Eurasia. The ferocity of the conquest and the confusion of early rule exacerbated an agricultural decline already deepened by decades of internal warfare. For artisans and merchants, however, the period brought significant new opportunities." (emphasis mine)
