Hi Lorenzo,
you're right that we should stick to the same terminology between the online documentation and the code, otherwise it's confusing. In this case, though, a lower numeric timestamp is equivalent to an older event. The older an element is, the lower is its timestamp.
However, there is a another problem with the formulation. In the first sentence it's said no event with a lower (=older) timestamp whereas in the second sentence it's additional said that no event with the same timestamp as the watermark will be emitted. This is not consistent. We'll fix that.
Cheers,
Till