Age-dating and weighting stellar populations in galaxies at various cosmic epochs are essential steps to study galaxy formation through cosmic times. Evolutionary population synthesis models with different input physics are used towards this aim. In particular, the contribution from the thermally pulsing asymptotic-giant-branch (TP-AGB) stellar phase, which peaks for intermediate-age 0.6-2 Gyr systems, has been debated upon for decades. Here we report the detection of strong cool star signatures in the rest-frame near-infrared spectra of three young (~1 Gyr), massive (~10^10 Msun) quiescent galaxies at large look-back time, z=1-2, using JWST/NIRSpec. The co-existence of oxygen- and carbon-type absorption features, spectral edges and features from rare species such as Vanadium, and possibly Zirconium, reveal a strong contribution from TP-AGB stars. Population synthesis models with significant TP-AGB contribution reproduce the observations considerably better than those with weak TP-AGB, which are those commonly used. These findings call for revisions of published stellar population fitting results, pointing to lower masses and younger ages, with additional implications on cosmic dust production and chemical enrichment. These results will stimulate new generations of improved models informed by these and future observations.