It looks like the error they made was this: They added too much latency because they forgot to account for the latency they added in the client. You can see from their architecture diagram (Figure 4) that the latency measurement didn't include the client delay.
https://images.contentstack.io/v3/assets/bltad9188aa9a70543a...
The blog post states: "The existing network monitoring system measured the latency at the networking layer as shown by the green arrow."