Intensity stability and wavelength correlations of near-infrared supercontinuum generation are studied in all-normal flattened dispersion, all-solid soft glass photonic crystal fiber. We use dispersive Fourier transformation method to measure shot-to-shot resolved spectra under pumping from a sub-picosecond, fiber-based chirped pulse amplification (CPA) system. For the first time to our knowledge, we demonstrate how unconverted radiation from pump, propagating in the photonic cladding of the fiber, improves the measured degree of coherence in the spectrum and influences its wavelength correlation by seeding of multiple four-wave-mixing / Raman scattering components. The presented results suggest a convenient and simple way of stabilizing of shot-to-shot coherence in sub-picosecond fiber laser pumped, normal-dispersion supercontinuum sources by direct, pump-related seeding.