Low fertility rates mean the death rate will be higher than the birth rate in the future. But not necessarily right now.

Imagine I build 100 robots, who will each live precisely 100 years. One robot chooses to build a replacement for itself, the rest do not. For 100 years, the death rate will be 0, and the birth rate will be 1. So more births than deaths. But the fertility rate is 0.01, so in 100 years the first generation will all die. Today the birth rate is higher, but low fertility means it'll be lower eventually.