Tiered negative interest rates are just a mirror-image of required reserves with positive interest rates.
Think back to the olden days. Interest rates were always positive, except for currency that paid 0% interest, and banks had minimum required reserves. So for a 10% required reserve ratio, for every $100 of demand deposits banks the banks were allowed to earn positive interest on $90 in loans, but had to keep $10 currency in the basement earning 0%.
Except having all that currency in the basement was an open invitation to robbers, so the bank deposited it at the central bank, in an account that paid 0%. Any bank going below that minimum could either borrow from another bank, or from the central bank, at a positive interest rate.
Required reserves were a tax on banks. They earned 0% on those minimum required reserves instead of some positive interest rate.
Now lets go to Denmark, Switzerland, or Japan. It's just like a mirror image of the olden days. Interest rates are negative, except for currency that pays 0% interest, and banks have maximum allowed reserves. They are allowed to keep a maximum amount of currency or deposits at the central bank earning 0%. Any bank going above that maximum can either lend to another bank, or to the central bank, at a negative interest rate.
Tiered negative interest rates are a subsidy on banks. They earn 0% on those maximum allowed reserves instead of some negative interest rate.
In both cases, what matters is the marginal interest rate. In the olden days we called it Open Market Operations when the central bank bought or sold bonds. Nowadays we call it "Quantitative Easing" when the central bank buys bonds (and negative QE when it sells bonds). Silly new name for a very old thing. By using OMO/QE the central bank can push or pull banks from the 0% interest margin to the positive or negative interest rate margin. With tiered negative rates, plus QE, commercial banks are pushed onto the negative interest margin.
If currency paid a market rate of interest, either positive or negative, none of this would matter. But with the nominal interest rate on currency stuck at 0%, government is collecting a tax on holding currency if market rates are positive, and paying a subsidy on holding currency if market rates are negative. So the minimum required reserves in a positive interest world, and the maximum allowed reserves in a negative interest world, level the playing field between banks and currency, but unlevel the playing field between banks and non-banks.
Everything old is new again, only it's a mirror image.