How does AWS DMS on-going replication works internally?
The reason you didn't find any specific information in AWS's documentation on the replication rate is because it mostly depends on the source database. For example, in Microsoft SQL Server, there's a feature called Change Data Capture (CDC) which logs data changes in real-time. This means DMS will gather all logs from the CDC tables in the source Microsoft SQL Server database since the last time DMS ran.
Other database systems might log changes at slower rates, so there isn't once answer from AWS's perspective. Additionally, I believe you can schedule DMS Tasks to run at their own intervals as well.
But in general, the goal of AWS's DMS Tool is to replicate all changes since it last synced.