I think your source is actually a bit misleading on the timeline for the narcolepsy cases. I can't find data for Finland but there is some for the UK in this paper:

https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1003225

"Onset of symptoms" for something like narcolepsy doesn't tell us much. One might assume that means narcolepsy was diagnosed and registered as a side effect, authorities notified, etc. within roughly 7 weeks. The problem is that the time from onset of symptoms to diagnosis for something like narcolepsy is usually years. So we wouldn't even have narcolepsy reported as a side effect until then.

Figure 3 in that paper shows the timeline from symptom to first contact with the healthcare system to diagnosis. The median time to contact is about 6 months, then another year for diagnosis. That's actually quite fast for a narcolepsy diagnosis; the average time in the US is 5-10 years. This is likely because the UK has a socialized medical system so patients are less concerned about the cost of the dozens of appointments it usually takes to get a diagnosis.