"Rapid population ageing" is a shorthand for an increase in the age distribution of the population. In itself this cannot cause population growth. It is necessary (mathematically) that the crude death rate (CDR) be below the crude birth rate (CBR). The CDR is deaths per one thousand people per year (as it is usually expressed), and CBR is live births per thousand per year.
Consider the extreme example where the CBR is zero. The fact that the living folks age, and on average are older, does not increase the population. In fact you could imagine an indefinite increase in longevity without any increase in population if you had no live births (and no net migration).
In developed countries at the present time, the CDR is below the CBR. Given the age distribution of the population and a CBR below replacement, eventually the population is going to decline. Also, the CDR will increase even though people live longer.