In the quest for efficiency and performance, edge-computing providers replace process isolation with sandboxes, to support a high number of tenants per machine. While secure against software vulnerabilities, microarchitectural attacks can bypass these sandboxes. In this paper, we present a Spectre attack leaking secrets from co-located tenants in edge computing. Our remote Spectre attack, using amplification techniques and a remote timing server, leaks 2 bit/min. This motivates our main contribution, DyPrIs, a scalable process-isolation mechanism that only isolates suspicious worker scripts following a lightweight detection mechanism. In the worst case, DyPrIs boils down to process isolation. Our proof-of-concept implementation augments real-world cloud infrastructure used in production at large scale, Cloudflare Workers. With a false-positive rate of only 0.61 %, we demonstrate that DyPrIs outperforms strict process isolation while statistically maintaining its security guarantees, fully mitigating cross-tenant Spectre attacks.