Recently, the growing demand for customized products and advances in smart technologies have accelerated the shift toward cloud manufacturing (CMg). Although CMg offers high flexibility, its dynamic nature introduces major scheduling challenges, such as new task arrivals and strict delivery constraints, which are often overlooked in existing models. To address these limitations, this study formulates a dynamic scheduling problem in CMg (DSPCMg) that integrates new task arrivals with the objective of minimizing delivery time deviations. Given the NP-hardness of the problem, five well-established metaheuristic algorithms are implemented, and six hybrid algorithms are developed to achieve a better balance between global exploration and local exploitation. In addition to modeling dynamic task arrivals, the proposed framework incorporates sequence-dependent setup times, delivery time windows, and logistics considerations within a unified formulation. The performance of the proposed algorithms is evaluated using test problems and 30 benchmark instances for both the scheduling and rescheduling stages. Computational experiments show that the hybrid KA-TS algorithm achieves the best performance in the scheduling stage, whereas GA-TS performs best in rescheduling scenarios. Moreover, the proposed rescheduling approach reduces delivery deviation by up to 45% and machine idle time by up to 32% compared with fixed initial schedules. Finally, sensitivity analysis further highlights that increases in logistics times and the number of new tasks significantly raise delivery time deviations.