Residence/ward/jumin tax in Japan

Hi,

I'd like to know how this tax works. I've heard you don't pay it in your first year, but it's calculated from 1st Jan to 31st Dec each year, so how does it work?

Let's say I started a job 1st November 2019. On 1st January 2020 I live in Shinjuku-ku. Do they need to know those two month's salary to charge me on it in Feb-March and I pay that off during the year?

And then if I continue to live in Japan and earning a salary? Let's say January 1st 2021 I still live in Japan, are the only charging me on 2020's salary? Or also the small 2019 salary (in the case that they didn't charge me tax the first year).

Sorry, I have read so many online posts about this and they're not very useful in giving
proper examples like this, they refer to different timings and appointing people to sort out your tax but I don't know at what point you're supposed to file.

Thank you in advance!