Something still seems strange in your description, although I’m not sure what it is.
On my (Canadian) pay stub, there’s a contribution to the DB pension plan. At the end of the tax year, we claim that amount to reduce our taxable income, because it will be taxed when we receive the income from the pension (ie. tax deferred). Otherwise, it would be double taxed, which would not encourage people to put money into retirement vehicles.
However, the employer knows that, so they reduce the amount of taxes they withhold from the paycheque by a commensurate amount. If they didn’t, I’d get a much larger tax return at the end of the year.
The pension contribution does reduce the allowable contribution room in other retirement accounts.
So it sounds like you’ll be double-taxed on your pension contributions? Once when you put it in, later on the pension income? I think that’s what seems strange.