A hot-state signal relaxes the moment treatment ends. The in-situ observer reads it at t = 0; the ex-situ observer reads whatever survives the journey.
Schematic single-exponential relaxation M(t) = M∞ + (M0 − M∞)·e−t/τ with a 25-minute teaching τ toward a 20% residual. This is a single-exponential model; real systems may show multiple relaxation times, intermediates or irreversible pathways, and relaxation times range from “effectively never” to seconds — and are usually unknown in advance, which is the argument for looking in place first.