AWS Direct Connect makes it easy to establish a dedicated network connection from your premise to AWS. Using AWS Direct Connect, you can establish private connectivity between AWS and your datacenter, office, or colocation environment [...]Specifically, of course, the observation is that as used in this context, the term should be premises, as per the second definition here:
It seems possible to me that premise in the usage above might be an example of a singular back-formation from what is in effect a mass noun (premises), along the lines of pease > peas > pea. (See also cherry.) Thus, premises in this context is being interpreted as a plural—We visited the company's [many] premises.
If this analysis is true, it seems like the tendency to think of the land-oriented premise as singular might be helped along by the existence of premise as an existing singular, albeit with a different meaning.
Someone else pointed out that the term on-premise has some traction. Assuming that Mr. Google is correctly interpreting my query, that term seems to have been a variant with equal frequency for a while of on-premises: