the cause of the would-be war is that the two sides could not agree whether or not they are the same country. By calling it a "civil war" you just dismissed the whole point of it.

also ethnicity has nothing to do with sovereign, nor that it exists a single "China" ethnicity, for Taiwanese people (who themselves are not a single ethnicity) to be lumped into. China just like all countries in the world, has many ethnicities.

The simple answer for your question is, because one side asked, and this kind of intervention has countless precedence in geopolitics. I reckon China probably has asked for external help several times in its history.