Thanks for all your advice - I am just a beginner and was worried that I do something wrong. If it is just the way wind instruments work I will find a way to solve the watering problem (shaking, blowing, swabbing, towel-protecting my trousers, ...)

After all your explanations, the physics of what happens is clear, also that it is unavoidable (but perhaps reducible).

Melani, if I understand you correctly, I should heat up the whistle to a temperature above the temperature of my breath to avoid the problem. But that might lead to a different question: what can I do to protect my lips and fingertips from getting burned? ;-)