The tea cools mostly by evaporation - when you pour it into two cups you will have twice the surface area.
During evaporation, the fastest (hottest) water molecules escape the liquid, leaving on average a cooler liquid behind (when the richest man leaves the room, the average wealth in the room drops).
The "evaporation cools down tea" concept is well known by Indias Chai Wallahs - see for example this video. There are more spectacular examples but I could not locate one right now.
There is a secondary effect of heat capacity: when you pour tea into a cold cup, some of the heat in the tea is used to warm up the cup. Two cups to warm up = more heat extracted from the tea. But that is a one time effect. The evaporation keeps going.
One other reason why the chai wallah trick is so effective (and why blowing on your tea cools it more quickly): as water evaporates, it increases the partial vapor pressure right next to the liquid. If that vapor is not removed, the result is that evaporation (and cooling) slows down. The pouring trick ensures the vapor can escape easily - the liquid is always surrounded by fresh (somewhat dry) air. Note that even if you do this in highly humid air (relative humidity 95%), since the tea is hotter than the air it heats the local air which allows more vapor to go into it. But the rate of cooling will be greatest when the air is driest. Within limits, that is more important than how cold the air is.