Splitting tea is extremely common in Mumbai. Actually it is possible to order only "Half cup" of Tea (Chai). The term to use is "cutting" or to order - Ask for "Cutting Chai". The term cutting signifies the tea is cut in half and only half a cup is served. Of course the price is significantly lower than a full cup of chai (usually half the price as well).

Just google "cutting chai" or "Cutting tea"

https://www.quora.com/What-is-a-cutting-chai

So in the OPs instance, it would have been possible to just order half the cup (and pay for half the cup!)