Global warming poses a threat to winemaking worldwide, especially in dry–warm regions such as Southern Italy. Must fermentation with non-Saccharomyces yeast starter is a possible approach to limit the negative effects of climate change, leading to desirable effects such as an increase in total acidity and/or aroma improvement. The aim of this study was to evaluate the effects of the use of a non-Saccharomyces starter (Lachancea thermotolerans) on the chemical and sensory properties of wines obtained by the the fermentation of two autochthonous Apulian grape cultivars, namely Bombino nero and Minutolo, as compared to the traditional Saccharomyces cerevisiae-driven fermentation. Bombino and Minutolo wines fermented with either Lachancea thermotolerans or Saccharomyces cerevisiae were characterized for their oenological parameters, volatile profiles, and sensory properties. Both chemical and sensory properties were affected by the yeast starter. Inoculation of L. thermotolerans increased sensory complexity, with different floral and sweet-like attributes for both cultivars. Bombino nero, a neutral cultivar, showed a clear effect on wine composition, with both an increase in lactic acid and a change in the volatile profile. On the contrary, the impact of L. thermotolerans was partially masked in Minutolo due to the strong primary aroma background of this highly terpenic cultivar. In this work, we evidenced a notable cultivar × yeast interaction, showing how generalizations of the effects of non-Saccharomyces yeasts on vinification are difficult to achieve, as they show a cultivar-specific outcome.