The need for effective public health surveillance systems to track virus spread for targeted interventions was highlighted during the COVID-19 pandemic. It spurred an interest in the use of spatiotemporal clustering and genomic analyses to identify high-risk areas and track the spread of the SARS-CoV-2 virus. However, these two approaches are rarely combined in surveillance systems to complement each one's limitations; spatiotemporal clustering approaches usually consider only one source of virus transmission (i.e., the residential setting) to detect case clusters, while genomic studies require significant resources and processing time that can delay decision-making. Here, we clarify the differences and possible synergies of these two approaches in the context of infectious disease surveillance systems by investigating to what extent geographically-defined clusters are confirmed as transmission clusters based on genome sequences, and how genomic-based analyses can improve the epidemiological investigations associated with spatiotemporal cluster detection. For this purpose, we sequenced the SARS-CoV-2 genomes of 172 cases that were part of a collection of spatiotemporal clusters found in a Swiss state (Vaud) during the first epidemic wave. We subsequently examined intra-cluster genetic similarities and spatiotemporal distributions across virus genotypes. Our results suggest that the congruence between the two approaches might depend on geographic features of the area (rural/urban) and epidemic context (e.g., lockdown). We also identified two potential superspreading events that started from cases in the main urban area of the state, leading to smaller spreading events in neighboring regions, as well as a large spreading in a geographically-isolated area. These superspreading events were characterized by specific mutations assumed to originate from Mulhouse and Milan, respectively. Our analyses propose synergistic benefits of using two complementary approaches in public health surveillance, saving resources and improving surveillance efficiency.