IceAct is a proposed surface array of compact (50 cm diameter) and cost-effective Imaging Air Cherenkov Telescopes installed at the site of the IceCube Neutrino Observatory at the geographic South Pole. Since January 2019, two IceAct telescope demonstrators, featuring 61 silicon photomultiplier (SiPM) pixels have been taking data in the center of the IceTop surface array during the austral winter. We present the first analysis of hybrid cosmic ray events detected by the IceAct imaging air-Cherenkov telescopes in coincidence with the IceCube Neutrino Observatory, including the IceTop surface array and the IceCube in-ice array. By featuring an energy threshold of about 10 TeV and a wide field-of-view, the IceAct telescopes show promising capabilities of improving current cosmic ray composition studies: measuring the Cherenkov light emissions in the atmosphere adds new information about the shower development not accessible with the current detectors, enabling significantly better primary particle type discrimination on a statistical basis. The hybrid measurement also allows for detailed feasibility studies of detector cross-calibration and of cosmic ray veto capabilities for neutrino analyses. We present the performance of the telescopes, the results from the analysis of two years of data, and an outlook of a hybrid simulation for a future telescope array.