So the assumption is that some populations will always reproduce in sufficient numbers and immigrate, and this just goes on forever and everything’s fine? Those other populations never age and decline?

That is _one_ assumption.

Another is that immigrants into these countries can and will just plug right into the local economy and be adequate substitutes for the economic effects of the local population decline.

There's everything about a country unrelated to economics that isn't even addressed too that will likely have ... big implications for these countries receiving the mass immigration too. These will likely also affect the economy.

The paper explicitly states that global population decline is not being projected.

Obviously that can't be true "forever" assuming that trends never reverse, but their scope is just the "long-term."

That sums up the ideology: That some ethnicities should continuously replace other ethnicities until the latter group has been genetically exterminated.