Your assumption was correct.
I knew most of that information already but the details of his arrival and departure dates from New Zealand are something I have been after for a while.
The Crimean service confuses me somewhat. The story in the family has always been that he was promoted without purchase to lieutenant following the mention in dispatches and later given a choice of regiments, following which he chose the vacant post of Lt. Paymaster in the 1/12th. This cannot be completely correct as he was promoted before the Crimea, but I have never heard about any purchase other than that of his ensign's commission in the 91st (which cost his father £1000). I have been led to believe that he transferred to the Buffs for some time in the Crimea and was mentioned in dispatches whilst serving with them (I have not checked Harts for this yet though). I also have a 1903 newspaper clipping of an obituary for my Great Grandfather Herbert (Col. Sir Walter's youngest son, who was killed in 1903 in Somaliland) which states that Col. Sir Walter "distinguished himself in the Commissariat during the Crimean War." Thus I am stumped as to why no edition of Harts I have yet seen mentions his service in the Crimea. Even if the story of him being in the Buffs for a time turned out to be wrong, the 1/91st were present in the Crimea, albeit on a nearby island managing a supply depot.