(And this includes the New Zealand dollar price of things which could be exported, such as milk and meat, because the prices of goods of this kind are also directly affected by the depreciation of the exchange rate.) These price rises will not happen instantaneously, particularly where importers and exporters have covered their foreign exchange risk in the forward market.
This situation might allow more liquid monetary conditions than would otherwise be the case. Distinguishing the various forces in play obviously requires tools that are finer than simple observations that both liquidity measures and assets prices are moving together.