Many of these events (e.g., the Medieval Climate Anomaly or the Roman Warm Period, etc.) are better described as "patchy" as opposed to global. Both the MCA and RWP were the most intense in the northern hemisphere, and specifically in portions of western Europe. This does not mean that there were no effects elsewhere, but these were generally less extreme and the global effects were (1) asynchronous, (2) differed in magnitude, and (3) sometime even differed in sign (i.e., in some places the MCA or RWP represented anomalously cool periods). This is discussed in lay terms moderately well in this Skeptical Science post, but it's a bit dated. There are however more recent papers highlighting the same point (e.g., Neuokm et al., 2019). Thus, in the context of comparing events like the MCA or RWP to modern conditions, they break down pretty quickly because in the modern anthropogenically induced warming, we consistently see rapid warming pretty much everywhere globally and synchronously (and specific to the New Zealand example, follow up work - e.g., Lunning et al., 2019 - has specifically highlighted that while the MCA is recognizable in records through much of Oceania, it's not exactly synchronous, appearing to occur up to several hundred years later in different areas). So, in the form of a direct response, finding that the MCA represented a warm period in 2 places (i.e., western Europe and Oceania) within a broad band of time, does not imply that it's a global event in the same sense as what we are seeing today.