We present rigorous experimental studies on the spectral and temporal behaviors of an erbium-doped frequency-shifted-feedback fiber laser (FSFL), with respect to various parameters of the laser cavity, including the direction of the frequency-shift mechanism, the quantity of frequency-shift, and the output coupling ratio (OCR) of the cavity. We show that if the filter bandwidth is much broader than the laser linewidth, the laser spectrum tends to split and form a secondary spectral band (SSB) on the shorter or longer wavelength side of the primary spectrum, depending on whether the direction of the frequency-shift mechanism is upward or downward, respectively. We found that the SSB forms a parasitic pulse with much lower peak power traveling on the leading or trailing edge of the primary pulse, which leads to a significant asymmetry in the whole pulse formation in the time domain.