  We present and investigate two issues within the measurement scheme for QFT
presented by J. Polo-G\'omez, L. J. Garay and E. Mart\'in-Mart\'inez in "A
detector-based measurement theory for quantum field theory". We point out some
discrepancies that arise when the measurement scheme is applied to contextual
field states and show that $n$-point function assignments based on local
processing regions sometimes lead to inconsistencies. To solve these issues, we
modify the measurement scheme to use non-relativistic detectors to induce an
update rule for algebraic states in the Haag-Kastler formulation of quantum
field theory. In this way, $n$-point functions can be consistently evaluated
across any region having a definite causal relation with measurements.
