premise.
noun
1.

Also, premissLogic. a proposition supporting or helping to support a conclusion.
premises.
noun
  1. a tract of land including its buildings.
  2. a building together with its grounds or other appurtenances.
  3. the property forming the subject of a conveyance or bequest.

See the difference? Something that’s on-premise is something which is aligned to the original proposition or logic. Something that’s on-premises is located on-site. if you insists, because I know how you kids are with the shortcuts these days, on-prem can be a shortened version of on-premises. 

But do not say “on-premise” to mean “on-site.” Correct other people who make this mistake. We will not lose this battle!