We present a time-dependent density functional theory (TDDFT) study on the electron dynamics of small carbon clusters C-n (n = 9, 10) exposed to a linearly polarized (LP) or circularly polarized (CP) oscillating electric field of ultrafast laser with moderate laser intensity. The multielectron dynamics is described by propagating the reduced one-electron density matrix in real-time domain. The high harmonic generation (HHG) spectra of emission as well as the time evolution of atomic charges. dipole moments and dipole accelerations during harmonic generation are calculated. The microscopic structure-property correlation of carbon chains is characterized. It is found that the electron responses of C-n to the laser field oscillation become nonadiabatic as the field intensity is larger than 1.4 x 10(13) W/cm(2). The nonadiabatic multielectron effect is displayed by an explicit fluctuation on the induced atomic charges and the instantaneous dipole acceleration and by observing the additional peaks other than those predicted from the spectral selection rule in HHG spectra of C-n as well. The origin of these additional peaks is elucidated. The atomic charges of C-n in LP and CP laser pulses experience different type of oscillations as expected. In the linear structure C-9, the atomic charges at the two ends experience larger amplitude oscillations than those near the chain center whereas the induced charges on each atom of C-10 experience the equal amplitude oscillations in the CP laser pulse.