A whole month of pension to pay for the few days before my job started?

Context: Last year, I left the country to go from a Working-Holiday Visa to a Work Visa and I came back to Japan on October 23rd.
I took a few days to get all the paperwork sorted and started joined my company on November 5th.
Naturally, my company covers my insurance, my pension, etc.

Now, I went to my local pension service today as I noticed a mistake in the category they put me in (they put me in the Student / Unemployed category by default since I failed to make my declaration at the time because the papers arrived at my previous adress and I only retrieved them recently thanks to my previous management company).

So, they fixed the problem alright, I managed to update my adress, so all is fine on this side. But they're now asking me to settle my pension for the month of October (for which I was in Japan for about a week (October 23rd to 31st), as I wasn't covered by my company yet, which is of 16,980 yen.

Is it a shouganai moment and there's no way I can get a pro-rata and not pay the whole month, or are they messing with me just to make me pay more and there is usually a way to accomodate this ?

Thanks in advance!