Fifth generation (5G) networks are expected to connect a huge number of Internet of Things (IoT) devices in many usage scenarios. The challenges of typical massive IoT applications with sporadic and short packet uplink transmissions are well studied, while not enough attention is given to the delivery of content of common interest, such as software/firmware updates and remote control, towards IoT devices in emerging point-to-multipoint scenarios. Moreover, the delivery of delay-sensitive IoT traffic is not sufficiently addressed in the literature. In this work we (i) identify the drawbacks of the current Single-Cell Point-to-Multipoint (SC-PTM) solution for unplanned critical traffic delivery in cellular IoT (cIoT) networks, and (ii) propose paging and multicast schemes for a fast distribution of critical updates after, e.g., bug fixes or system failures. We benchmark the performance of the proposed paging scheme against similar solutions available in the literature. Our extended SC-PTM framework is energy efficient and guarantees low service latency, as demonstrated both analytically and by simulations. © 2020