Many economists claim that social security reduces fertility for complicated reasons involving old age security- and not the obvious one, that social security is transfer from young fertile populations to older infertile populations. One such paper is shown below. It studies the effect of the 1992 Amato and 1995 Dini reforms.
They provide details of the reforms in the below table.
The main effect of the reforms was to decouple benefits from real wages. If Italian workers correctly expected real wages to fall in the second half of the 90s, then they are actually better off under the new system- contrary to what the authors imply.
Consider also this IMF paper:
So the second reform is potentially better for those subject to it as well.
In conclusion, the authors do not present a compelling case that the reforms were expected to reduce benefits during the period the authors studied.