Systematic calculations on the spectroscopy and transition properties of even-even Te isotopes are carried out by using the large-scale shell-model configuration-interaction approach with a realistic interaction. These nuclei are of particular interest since their yrast spectra show a vibrational-like equally spaced pattern whereas the few known $E2$ transitions show rotational-like behavior. This cannot be explained by available collective models. My calculations reproduce well the equally spaced spectra of those isotopes as well as the constant behavior for the $B(E2)$ values of $^{114}\mathrm{Te}$. The calculated $B(E2)$ values of neutron-deficient and heavier Te isotopes show contrasting different behaviors along the yrast line. The $B(E2)$ of light isotopes can exhibit a nearly constant behavior up to high spins. It is shown that this is related to the enhanced neutron-proton correlation when approaching $N=50$.