The unchecked spread of misinformation is recognized as an increasing threat to public, scientific and democratic health. Online networks are a contributing cause of this spread, with echo chambers and polarization indicative of the interplay between the search behaviours of users and reinforcement processes within the system they inhabit. Recent empirical work has focused on interventions aimed at inoculating people against misinformation, yielding success on the individual level. However, given the evolving, dynamic information context of online networks, important questions remain regarding how such inoculation interventions interact with network systems. Here we use an agent-based model of a social network populated with belief-updating users. We find that although equally rational agents may be assisted by inoculation interventions to reject misinformation, even among such agents, intervention efficacy is temporally sensitive. We find that as beliefs disseminate, users form self-reinforcing echo chambers, leading to belief consolidation-irrespective of their veracity. Interrupting this process requires 'front-loading' of inoculation interventions by targeting critical thresholds of network users before consolidation occurs. We further demonstrate the value of harnessing tipping point dynamics for herd immunity effects, and note that inoculation processes do not necessarily lead to increased rates of 'false-positive' rejections of truthful communications.