The emergence of localized structures originating from instabilities is of particular interest to scientists interested in exploring the rich nonlinear dynamics associated with complex dynamical systems. In the context of ultrafast lasers, the localized structures can be broadly divided into two categories: coherent structures of the dissipative soliton (DS) and incoherent structures such as the noiselike pulse (NLP). These two different types of structures have unique properties and applications and their physical origins are markedly different. Having both in a single fiber laser is an intriguing but challenging problem. Here we demonstrate the formation of the DS and NLP in a bidirectional ultrafast fiber laser and study their buildup dynamics from Q-switched instabilities. The clockwise light is a DS while the counterclockwise light is a NLP. The synchronized buildup dynamics of a DS or NLP from Q-switched instabilities provides vital evidence of the Q-switched instabilities as a universal indicator for the generation of localized structures in ultrafast lasers. The evenly spaced Q-switched spikes before the onset of a DS (NLP) exhibit intensity fluctuations, which is strikingly different than in the mode-locking regime in unidirectional oscillators, hence providing decisive evidence of the interaction between the counterpropagating light fields in the bidirectional lasers. The spectra cross-correlation and the histogram of the spectral intensity confirm the concurrent formation of a DS and NLP. Numerical simulations confirmed experimental observations. These findings help deepen understanding of the behavior of bidirectional ultrafast lasers and also demonstrate their potential as multifunctional ultrafast laser sources. © 2022 American Physical Society.