The goal of this work was to apply ionic liquids (ILs) with bis(trifluoromethylsulfonyl)imide anion (TFSI) for fine-tuning the cure characteristics and physico-chemical properties of elastomer composites based on a biodegradable natural rubber (NR) matrix. ILs with TFSI anion and different cations, such as alkylpyrrolidinium, alkylammonium, and alkylsulfonium cations, were applied to increase the efficiency of sulfur vulcanization and to improve the performance of NR composites. Thus, the influence of ILs on the vulcanization of NR compounds, as well as crosslink density and physical properties of NR vulcanizates, including tensile properties, thermal stability, and resistance to thermo-oxidative aging was explored. The activity of ILs seems to be strongly dependent on their cation. Pyrrolidinium and ammonium ILs effectively supported the vulcanization, reducing the optimal vulcanization time and temperature of NR compounds and increasing the crosslink density of the vulcanizates. Consequently, vulcanizates with these ILs exhibited higher tensile strength than the benchmark without IL. On the other hand, sulfonium ILs reduced the torque increment owing to the lower crosslinking degree of elastomer but significantly improved the resistance of NR composites to thermo-oxidation. Thus, TFSI ILs can be used to align the curing behavior and performance of NR composites for particular applications.