Laser frequency microcombs provide a series of equidistant, coherent frequency markers across a broad spectrum, enabling advancements in laser spectroscopy, dense optical communications, precision distance metrology, and astronomy. Here, we design and fabricate silicon nitride, dispersion-managed microresonators that effectively suppress avoided-mode crossings and achieve close-to-zero averaged dispersion. Both the stochastic noise and mode-locking dynamics of the resonator are numerically and experimentally investigated. First, we experimentally demonstrate thermally stabilized microcomb formation in the microresonator across different mode-locked states, showing negligible center frequency shifts and a broad frequency bandwidth. Next, we characterize the femtosecond timing jitter of the microcombs, supported by precise metrology of the timing phase and relative intensity noise. For the single-soliton state, we report a relative intensity noise of -153.2 dB / Hz, close to the shot-noise limit, and a quantum-noise–limited timing jitter power spectral density of 0.4 as² / Hz at a 100 kHz offset frequency, measured using a self-heterodyne linear interferometer. In addition, we achieve an integrated timing jitter of 1.7 fs ± 0.07 fs, measured from 10 kHz to 1 MHz. Measuring and understanding these fundamental noise parameters in high clock rate frequency microcombs is critical for advancing soliton physics and enabling new applications in precision metrology.