What physically happens when foreign currency reserves change?
Typically foreign reserves will just be assets denominated in a foreign currency, most importantly government debt. Another popular reserve asset are IMF special drawing rights, which are convertible into currencies of member countries. I don't think there is any amount of physical cash currency in international reserves. You can see the makeup of US reserves here: https://www.treasury.gov/resource-center/data-chart-center/IR-Position/Pages/12302016.aspx

If the US treasury would decide to increase it's Yuan holdings, it will just buy bonds that pay are traded and denominated in Yuan.