From when and how will the fixed tax reduction of 40,000 yen per person “specified on the pay slip” be deducted? How to get deducted from “income tax” and “residence tax” that you seem to know but don't know

Flat-rate tax cuts begin in June.
At the Chief Cabinet Secretary's press conference held on 5/21, Chief Cabinet Secretary Hayashi Yoshimasa stated, “In addition to the spring battle wage increase, which reached a high level for the first time in 33 years, we would like to reduce income by 40,000 yen per person, income tax and resident tax, and support disposable income, leading to the realization of income that exceeds high prices.”
Also, regarding the description on the pay slip that was reported in some reports, Chief Cabinet Secretary Hayashi stated, “In order to lead to breaking away from the deflationary mindset, it is important for citizens to be able to feel the effects of such policies, and those responsible for withholding tax will clearly state the large income tax reduction amount on the pay slip.”