Networked systems operating under intermittent adverse conditions and long memory can remain stable on average while exhibiting rare but extreme trajectory-level excursions. We study linear regime-switching network dynamics with Volterra-type memory, formulated through a finite-dimensional lifted ordinary differential equation embedding. Despite finite-horizon annealed boundedness, we show that quenched amplification emerges generically from the interaction of regime persistence, memory accumulation, and non-normal lifted operator geometry. A lower bound on burst-size distributions reveals power-law tails whose exponent is determined by the ratio between unfavorable dwell-time rates and an operator-defined instantaneous growth parameter. This parameter is computable online via the Euclidean logarithmic norm of the lifted operator, yielding a practical early-warning indicator. Building on this structure, we introduce a dynamic data-driven intervention strategy that enforces contraction on demand along rare amplification channels, thereby shaping or truncating tail risk without altering exogenous regime statistics or typical system behavior. The results provide a geometrically grounded and operationally actionable framework for understanding and mitigating extreme events in memory-driven regime-switching systems.