I don't know how it's in Japan but in Austria neither the company nor the employee file taxes. There is a general tax withholding that you do as an employer for your employees but the taxes are filed automatically by the state.
You can then retroactively go in and modify that by doing a "Arbeitnehmerveranlagung" where you can claim modifications to your automatic tax filings.
This is a different process for when you are self employed and you actually file taxes from "scratch" which however is also a significantly simplified process.
This is effectively not very different than how it works for most people in the US. Yhe employer sends the government forms and funds for your estimated taxes, and at the end of the year the taxpayer files a return and gets a refund based on varying deductions.
You can then retroactively go in and modify that by doing a "Arbeitnehmerveranlagung" where you can claim modifications to your automatic tax filings.
This is a different process for when you are self employed and you actually file taxes from "scratch" which however is also a significantly simplified process.