How should I adjust data for both inflation and foreign exchange rate? I’m not sure if this is typically done, but suppose my data point is in 2013 JPY and I want to express in 2016 USD. Do I apply CPI to express data in 2016 JPY, and then apply exchange rate to 2016 USD? Or do I apply exchange rate to obtain 2013 USD first, then apply CPI to bring forward to 2016 USD? Or is this all redundant?
NO, it is not redundant. Controlling for nominal effects gives you a better picture, and makes more sense on a theoretical level. To transform assets into USD use

$\textit{asset}_{USD}=\frac{s_t P_{t,JPY}}{P_{t,USD}} \textit{asset}_{JPY}$ 

where the fraction is the real exchange rate, $P_t$ is the respective price level and $s_t$ the nominal exchange rate.

Alternatively, you can work with differences

$\Delta rer =\frac{\Delta s_t \pi_{t,JPY}}{\pi_{t,USD}}$.

Note that the real exchange rate is far from perfect, but it is common practice in macroeconomics. Also, it does not matter which transformation you do first, as its purely multiplicative.