Compensation of the intracavity dispersion in the mode-locked oscillator is known to be one of the most important factors for ultrashort pulse generation. However, recent investigations of a Yb-doped fiber mode-locked oscillator revealed that precise third-order dispersion (TOD) compensation is not always necessary for ultrashort pulse generation, owing to the strong nonlinearity that compensates residual TOD without reducing its spectral bandwidth. The origin of the nonlinear TOD compensation has remained unclear. To investigate the process in detail, we studied the pulse evolution inside a 30 fs Yb-doped fiber mode-locked oscillator both experimentally and numerically, and we found that the nonlinear phase shift with a temporally asymmetric pulse shape introduces an appropriate amount of TOD that exactly cancels the residual cavity dispersion.