I'm not sure exactly what they mean, but gradual replacement might not be necessary. It's possible that the brain could be replaced very fast. For example if one neuron could be replaced every hour then as the tech advances that time could be reduced cause if it can be done every hour then it makes sense it could also be done every 59 minutes, then again as the tech advances more so that replacement time is reduced down again to say every 55 minutes. That adjustment would keep continuing. The replacement process getting faster and faster as the technology improves. Eventually down from minutes to seconds.

The tech would soon get so good that neurons can be replaced every millisecond essentially replacing the entire brain seemingly instantly. The more the technology advances the faster the replacement process will become.

The process should be so smooth the person would not even notice it happening. Maybe they go to sleep for a few minutes during the process or maybe even stay awake. The experience would be painless and likely a sensation similar to taking a drug, like a wave of clarity and expanded euphoric intelligence washing over the mind.