How do you properly store tins of turpentine?
In a general sense it is a very good practice to refer to the material safety data sheets (MSDS) for products like this. The product labels, in theory, should also contain similar information. 

MSDSs will always contain more information though. They will break down all the information needed about the product when it comes to safety. It should be safe to assume that householdproducts.nlm.nih.gov is a good source of this information. I located the sheet for your specific product. Most other MSDS's for turps cover the exact same sentiment as far as storage and handling is concerned. For completeness sake I have also included some basic handling as well in the information quoted below.


  HANDLING:
  
  
  Isolate from oxidizers, heat, sparks, electric equipment &amp; open flame. 
  Use only with adequate ventilation. Avoid breathing of vapor or spray mist. Avoid prolonged or repeated contact with skin. Wear OSHA Standard goggles or face shield. Consult Safety Equipment Supplier. Wear gloves, apron &amp; footwear impervious to this material. Wash clothing before reuse. 
  Avoid free fall of liquid. Ground containers when transferring. 
  Do not flame cut, saw, drill, braze, or weld. Empty container very hazardous! Continue all label precautions!
  
  
  STORAGE:
  
  
  Keep in fireproof surroundings. 
  Keep separated from strong oxidants, incompatible materials. Keep cool. Keep inside a well-ventilated room.
  Keep container tightly closed &amp; upright when not in use to prevent leakage.
  


Text is copied as is. Formatting and emphasis is my own.

Keep it cool, ventilated and away from sources of oxidants and sources of ignition. Ensure the container is seal and cleaned between uses. 



I am not sure about the cause of the leaking. Chris Johns has a good theory though. Assuming you follow the instructions above it should not happen. 

Related I found a discussion between users and the smells created by turpentine like yours and artist grade. Consensus is that the "cheap" stuff has a more offending odor