Earth-abundant kesterite Cu2ZnSnSe4 material is a promising candidate for the mass production of low-cost thin film solar cells. However, the synthesis of single-phase kesterite films is especially challenging, since the kesterite single-phase region in the equilibrium phase diagram is very narrow. In this study, the metal composition was varied within the Cu-poor composition range in order to study the presence of Sn-Se secondary phases. Both SnSe and SnSe2 are found in copper-poor CZTSe absorbers where Zn/Sn < 1; in addition, these phases are also found when Zn/Sn > 1 because the studied composition range is actually copper-poor zinc-rich and tin-rich. The Sn-Se secondary phases can be detected using X-ray diffraction, a bulk detection method. They are also detected at the absorber's surface by SEM and Raman spectroscopy. Therefore, when the Sn-Se phases are present, at least a part of them is located at the absorber's surface, which is highly detrimental to device performance. Acting as shunting paths, they reduce the device power conversion efficiency and demonstrate an apparent quantum efficiency effect under reverse bias. Removal of these phases from the surface by chemical etching greatly reduces their detrimental influence.