While APIM is a perfect choice for exposing services, doing so to just copy the database tables is not required. This would of course depend on how often you need to copy the database tables.
For bulk transfers, you could just make do with a simple script and/or program (any language) that could perform the move.
For periodic transfers, you could run the same script on a loop (keeping track of the last record synchronized) or use Logic Apps along with the On-Premises Data Gateway to transfer this data.
If your scenario would still benefit from exposing the APIs, you could leverage APIM by deploying into a Virtual Network that has access to your on-premises data via a VPN Gateway or ExpressRoute.