The machine (1) comprises: an unwinding section (3) of parent reels (Ba, Bb) of web material (Na, Nb); a cutting station (13), comprising a plurality of cutting members (201, 203) to divide the web material (Na, Nb) into longitudinal strips (S); a plurality of winding stations (15); in each winding station (15), a guide arm (31) to guide the longitudinal strip (S), adjustable parallel to the rotation axis (C-C) of the winding mandrel (51). The cutting station (13) comprises sensor members (213, 214) to detect the position of the cutting members (201, 203). A control unit (216) is interfaced with the sensor members (213, 214) of the cutting station (13) and the positioning actuators (27), to position the guide arms (31) parallel to the rotation axis (C-C) of the respective winding mandrel (51) as a function of the position of the corresponding cutting member (201, 203).