It is wise to be cautious about attributing a correlation to a cause and effect relationship. This is one instance where rather than simple cause -> effect it could be both cause AND effect. That is, if the cycling environment (laws, cyclist & motorist training, physical facilities ranging from traffic signals that give cyclists priority all the way to separate paths) is safer, more people cycle. As more people cycle and spend more hours cycling, more motorists & and cyclists are aware how to not have collisions.
The paper cites another study which implies that environment improvement sometimes may precede increased cycling: "...changes in numbers of bicyclists and collisions between motorists and bicyclists in response to changes in physical configuration at 45 non-signalized intersections between bicycle paths and roadways in Gothenburg, Sweden. The total number of collisions increased with the 0.4 power of the increasing use of the intersections by bicyclists."
However, regarding the data in his study he concludes "... possible explanations are changes in human behavior, roadway design, laws, and social mores. However, insofar as the changes seen in the time series data occurred rapidly and with both increasing and decreasing amounts of bicycling, it is improbable that the roadway design, traffic laws, or social mores, all of which change relatively slowly, could explain the relationship between exposure and injury rates. The more plausible explanation involves changes in behavior associated with changes in the amount of walking and bicycling." Thus his data suggest more cycling causing safer cycling.
So, I'd say it may be both cause and effect.