IRD doesn't just tack a redundancy payment onto your last payslip and tax it at whatever rate that pay period happens to land on. Instead it annualises your regular salary, adds the lump sum on top of that annualised figure, and finds a single marginal rate from the combined total. That one rate then applies to the entire lump sum, not to your regular pay, which stays taxed exactly as it always was.
This is why a large redundancy payment can look like it's taxed harder than your normal pay: if your regular salary already sits close to a bracket boundary, adding the lump sum on top pushes the combined figure into a higher bracket, and that higher rate applies to the whole payment, not just the amount technically over the line. It's a genuine consequence of how the "extra pay" method works, not an error or a penalty.
Redundancy payments and retiring allowances get two specific carve-outs that regular pay doesn't: no ACC Earner's Levy and no KiwiSaver deduction, regardless of how much you earn. That's different from a bonus, which does carry the ACC levy below the earnings cap, so don't assume every lump-sum payment from an employer gets the same tax treatment.