No need to worry. Canada does have a treaty with Japan to prevent double taxation. At tax time your spouse will declare their income as foreign employment income and enter the tax that has been deducted in Japan as a credit against that income.
One note: The income (and tax deducted) need to be entered in CAD. When it's time to file your returns, use the annual exchange rate listed here: https://www.bankofcanada.ca/rates/exchange/annual-average-exchange-rates/
The rate will be updated at the end of the year to reflect the average exchange rate for the whole year.
