Device (10) for packaging two products (A, B) separately and dispensing a resulting mixture (M) on a first use, comprising a lower container (12) delimiting a first product cavity (22) containing a first product (A) and an upper container (14) delimiting a second product cavity (24c) containing a second product (B), and being capable of rotating relative to the lower container (12) without moving axially, and a temporary closing member (30) configured to close an opened end (24b) of the upper container (14) before the first use, and comprising a cylindrical skirt (32) surrounding said opened end (24b) and a plug (34) connected to said cylindrical skirt (32), said cylindrical skirt (32) being designed to cooperate by thread engagement with the upper container (14) and being prevented from rotating relative to the lower container (12). The closing member (30) is deprived from any axially retaining members with both containers (12, 14), such that when the upper container (14) is rotated in a first rotation direction (F1), the closing member translates downwardly until falling into the first product cavity (22).