SARS-CoV-2 is a new pathogen responsible for the coronavirus disease 2019 (COVID-19) outbreak. Southeast Asia was the first region to be affected outside China, and although COVID-19 cases have been reported in all countries of Southeast Asia, both the policies and epidemic trajectories differ substantially, potentially due to marked differences in social distancing measures that have been implemented by governments in the region. This paper studies the across-country relationships between social distancing and each population's response to policy, the subsequent effects of these responses to the transmissibility and epidemic trajectories of SARS-CoV-2. The analysis couples COVID-19 case counts with real-time mobility data across Southeast Asia to estimate the effects of host population response to social distancing policy and the subsequent effects on the transmissibility and epidemic trajectories of SARS-CoV-2. A novel inference strategy for the time-varying reproduction number is developed to allow explicit inference of the effects of social distancing on the transmissibility of SARS-CoV-2 through a regression structure. This framework replicates the observed epidemic trajectories across most Southeast Asian countries, provides estimates of the effects of social distancing on the transmissibility of disease and can simulate epidemic histories conditional on changes in the degree of intervention scenarios and compliance within Southeast Asia.