We report on spectrotemporal transient dynamics in a femtosecond fiber-feedback optical parametric oscillator (FFOPO) system. Burst modulation of the pump beam in combination with dispersive Fourier transformation sampling allows to record single-pulse signal spectra at 41 MHz sampling rate. Therefore, each individual pulse of the signal transients can be spectrally resolved. We characterize the signal output behavior for anomalous as well as for normal intra-cavity dispersion. Amongst steady state output we observed period-doubling cycles and other attractors, which occured at higher intra-cavity nonlinearity levels. The experimental findings are supported by numerical simulations, in order to identify the linear and nonlinear effects, which govern the wavelength tuning behavior of this FFOPO system. We find that steady state operation is preferred and that the wavelength tuning stability of the FFOPO dramatically increases when using a normal dispersion feedback fiber.