I use both Chinese (pinyin) and Japanese (romaji) input and am used to having them mapped to a standard US keyboard layout.
However my regional setting is Switzerland since I'm studying here and “internet services may vary according to region”. Strangely, the Japanese input uses the US keyboard layout, but Chinese uses a European layout (not sure what, but z and y are switched). (Irrelevant to problem).
My inputs are, in this order:
English (US) German Japanese (Kotoeri) Chinese
As Tom pointed out, in Kotoeri's preferences the layout can be defined. The Chinese input however uses the last layout of a Latin input, in this case German.
There also doesn't seem to be an option to customise the order of these inputs. My workaround is to cycle backwards, but this obviously is a special case. If anyone has a better solution it would be appreciated.