Tissue products are described that have been topically treated with a chemical additive, such as a softener. The softener may be, for instance, a polysiloxane. The polysiloxane is topically applied to a tissue sheet, such as a single ply sheet, so as to form a Z-directional gradient in the sheet. Particular, most of the polysiloxane remains on the surface of the tissue product as opposed to migrating to the center of the sheet. In this manner, tissue sheets are formed with improved softness at lower levels of polysiloxane and without the need for applying any surfactants to the sheet. A system for applying chemical additives to tissue sheets is also described. The system includes a chemical additive applicator, such as a meltblown die that emits the chemical additive through a plurality of orifices. In one embodiment, the system includes a device for periodically cleaning the orifices during application of the chemical additive. The cleaning device may be, for instance, a brush that traverses across the die head when desired.