You’re halfway there.
There are more units, but the original holders of the units are getting the extra units. It is not being given out by a cental bankers.
Maybe a link to a known economics site helps, a stock split is extremely similar in nature.
A stock split is when a company divides its stock into multiple shares, effectively lowering the price of each share without changing the company’s market value. It’s akin to cutting a cake into smaller slices; you end up with more pieces, but the total amount stays the same.
The total value of the coin stays the same too. Every single user just has more units.
This needs repeating. There is no inflation in the subsatoshi setup because the money in your wallet gets more units. So unlike a politician using inflation to pay for government spending, no central agency or politician or even people here gets the extra coins. Not more than any single other holder gets.