It would seem that Johann Heinrich Schmelzer was familiar with it, since a (greatly expanded) German-language version of one of the pieces circulated under his name.
Johann Sebastian Bach | Johann Wolfgang von Goethe | Heinrich Himmler | Johann Strauss II | Heinrich Heine | St. Johann in Tirol | Heinrich Schütz | Johann Heinrich Pestalozzi | Heinrich von Kleist | Johann Albert Fabricius | Johann Christian Bach | Heinrich Böll | Johann Georg Wagler | Johann Pachelbel | Johann Nepomuk Hummel | Johann Gottfried Herder | Heinrich Isaac | Johann Nestroy | Heinrich Marschner | Baron Hans Heinrich Thyssen-Bornemisza | Johann Joachim Winckelmann | Johann Gottlieb Fichte | Johann Bernhard Fischer von Erlach | Johann Homann | Johann Friedrich Böttger | Heinrich Mann | Heinrich Hertz | Heinrich Graetz | Heinrich Böll Foundation | Christian Heinrich Friedrich Peters |
Some composers who specified the use of the cornettino in their scores include: Michael Praetorius, Heinrich Schütz, Johann Heinrich Schmelzer, Heinrich Ignaz Franz von Biber, Matthias Weckmann, Antonio Bertali, Johann Caspar Horn, Johann Erasmus Kindermann, Matthias Spiegler, Johann Vierdanck, Johann Sebastian Bach and Georg Philipp Telemann.
He may have been born in Milan, but first surfaces in Vienna, in a letter exchange between the famous violinist Johann Heinrich Schmelzer of the Viennese court and Karl II von Liechtenstein-Kastelkorn, Prince-Bishop of Olomouc.