Microsoft has provided rich support for Exchange on-premises to integrate with Exchange Online for several years. This coexistence is one of the major strengths of the Microsoft cloud solution as it allows customers to perform Digital Transformation at their own pace.
It is not expected that an organisation will transition all of their on-premises mailboxes overnight, that would be unrealistic for many Exchange deployments. While Exchange hybrid deployments have provided a robust deployment solution, there have been issues with the nomenclature used.
One of the issues which has not been fully addressed is people using incorrect terminology; insisting on using "on-premise". Regrettably this is all too common inside Microsoft as well. The steps to create the required rule to block this incorrect phrase are documented in Transport Rule To Force On-Premises Terminology.
While it is possible to manually create an Exchange Transport Rule (ETR) to remove such incorrect language this has proven to be onerous and not all companies have implemented the rule.
As a result the phrase "on-premise" has not yet been eradicated.
Upcoming Exchange Product Changes
Based on feedback from the field, and also internally, the above transport rule will be automatically created when the next Exchange 2013 or 2016 CU is installed if the required transport rule does not exist.
The intent is to enforce the correct grammar and use of on-premises in any an all communications. This is critical as since every time someone says "on-premise" a puppy dies.
Note that on-prem is acceptable and will not cause the ETR to be triggered.
Exchange 2010 is already in extended support and will not benefit from this feature.