After how long is boiled milk tea consumable?
Probably not. Perishable food and drinks are considered unsafe after being in the danger zone (40°F - 140°F, 5°C - 60°C) for more than 4 hours (EDIT: when I was a cook in Massachusetts, four hours was the cut off. Apparently the USDA recommends two hours). And note: that's a cumulative four hours over the course of the foodstuff's lifetime, not four hours in a row. If the milk sits on the counter for an hour, then it's boiled and put into tea which then sits out for three hours, it's considered unsafe.


  Leaving food out too long at room temperature can cause bacteria (such
  as Staphylococcus aureus, Salmonella Enteritidis, Escherichia coli
  *O157:H7*, and Campylobacter) to grow to dangerous levels that can cause
  illness. Bacteria grow most rapidly in the range of temperatures
  between 40 °F and 140 °F, doubling in number in as little as 20
  minutes. This range of temperatures is often called the "Danger Zone."
  
  Keep Food Out of the "Danger Zone"
  
  Never leave food out of
  refrigeration over 2 hours. If the temperature is above 90 °F, food
  should not be left out more than 1 hour.  Keep hot food hot — at or
  above 140 °F. Place cooked food in chafing dishes, preheated steam
  tables, warming trays, and/or slow cookers. Keep cold food cold — at
  or below 40 °F. Place food in containers on ice.


Also crucial to remember when food safety is concerned: FAT TOM. FAT TOM is a mnemonic device which stands for:


Food
Acidity
Time
Temperature
Oxygen
Moisture


All of those things are a factor in the growth of bacteria. With room-temperature milky tea that's been sitting out all day, we've got the full gamut:


Nutrients from the milk (food)
If it's milky tea, it you probably didn't put lemon in it, because let's face it, that'd be gross unless you have a thing for curdled milk.
Time - you said it's been there since this morning
Temperature - at room temperature
Oxygen - I doubt this is space tea or that it was stored in a vacuum.
Moisture - it's a cup of infused water and milk. Doesn't get much more moist than that.


Remember: When in doubt, throw it out.