One technique to mitigate this that does not require extraordinary care on the part of the installer is “flash and batt”: apply a thin layer of spray foam to the exterior wall and then fill the cavity with fiberglass, mineral wool or some other fluffy insulation. The spray foam adheres to the wall and leaves no space for humid air to reach, and the inner surface of the spray foam will stay warm enough to avoid condensation.
Frame first — you want the foam to stick to the exterior shell and to the framing members that are up against the exterior. Protect anything you don’t want foamed — the fresh foam sticks to everything and foam in your electrical boxes is no fun.
(The unreacted chemicals are not persistent — they’re too reactive to stick around.)