Spatial alarms extend the idea of time-based alarms to the spatial dimension. Just as time-based alarms are set to remind us of the arrival of a future reference time point, spatial alarms are set on a spatial location of interest which the subscribers of the alarm will travel to sometime in the future. Spatial alarm processing requires meeting two demanding objectives: high accuracy, which ensures zero or very low alarm misses, and high scalability, which requires highly efficient and optimal processing of spatial alarms. In this paper we present a motion-aware framework, facilitated by two systematic methods, for scalable processing of spatial alarms. First, we introduce the concept of safe period to minimize the number of unnecessary spatial alarm evaluations, increasing the throughput and scalability of the system. We show that our safe period-based alarm evaluation techniques can significantly reduce the server load for spatial alarm processing compared to the periodic evaluation approach, while preserving the accuracy and timeliness of spatial alarms. Second, we develop a suite of spatial alarm grouping techniques based on spatial locality of the alarms and motion behavior of the mobile users, which reduces the safe period computation cost for spatial alarm evaluation at the server side. We evaluate the scalability and accuracy of our approach using a road network simulator and show that the proposed motion-aware safe period-based approach to spatial alarm processing offers significant performance enhancements for the alarm processing server while maintaining high accuracy of spatial alarms, especially compared to the conventional periodic alarm evaluation approach.