You are correct. Currently, AppSync Subscriptions are only triggered from GraphQL Mutations. If there are changes made to the DynamoDB from a source other than AppSync, subscriptions will not trigger.
If you want to track all changes being made to DynamoDB table and publish them using AppSync, you can do the following:
1) Setup a DynamoDB stream to capture changes and feed the changes to AWS Lambda
https://docs.aws.amazon.com/amazondynamodb/latest/developerguide/Streams.html
https://docs.aws.amazon.com/amazondynamodb/latest/developerguide/Streams.Lambda.html
2) Setup an AppSync mutation with a Local (no datasource) resolver. You can use this to publish messages to subscribers without writing to a datasource.
https://docs.aws.amazon.com/appsync/latest/devguide/tutorial-local-resolvers.html
3) Make the DynamoDB Stream Lambda function (setup in step 1) call the AWS AppSync mutation (setup in step 2).
This will enable publishing ALL changes made to a DynamoDB table to AppSync subscribers, regardless of where the change came from.