Doubled compared to what?

This perhaps answers your question (although the length of the measurement intervals (before/after) is not specified):

When we launched, the number of people completing the form doubled.

How did 96% satisfaction get calculated earlier, if there were so many users whose needs were not met?

The 96% (or whatever the exact threshold is) seems to be a requirement imposed by law, so that it's probably measured through some external procedure:

Adding a lot of pressure, this was a regulated monopoly, and if their customer satisfaction dropped below 96% (if I remember correctly) it could result in millions of pounds in fines.