We determine the exact physical parameters of the four Hyades cluster K giants, using their parallaxes and atmospheric modeling of our red-channel TIGRE high-resolution spectra. Performing a comparison with well-tested evolutionary tracks, we derive exact masses and evolutionary stages. At an age of 588 (±60) Myrs and with a metallicity of Z=0.03 (consistent with the spectroscopic abundances), we find HD 27371 and HD 28307, the two less bright K giants, at the onset of central helium-burning, entering their blue loops with a mass of 2.62 M ⊙ , while the slightly brighter stars HD 28305 and HD 27697 are already exiting their blue loop. Their more advanced evolution suggests a higher mass of 2.75 M ⊙ .Notably, this pairing coincides with the different activity levels, which we find for these four stars from chromospheric activity monitoring with TIGRE and archival Mount Wilson data as well as from ROSAT coronal detections: The two less evolved K giants are the far more active pair, and we confidently confirm their rotation with periods of about 142 days. This work therefore provides some first, direct evidence of magnetic braking during the 130 Myrs lasting phase of central helium-burning, similar to what has long been known to occur to cool main-sequence stars.