The request parameter holds the information you are describing. Every field in a request has a corresponding parameter/visible_parameter column in the database (either in KCRT_REQUEST_DETAILS or KCRT_REQ_HEADER_DETAILS) to store values. With Table Components, another table was created to hold the different columns in the TC, but there is still data stored in the request parameter columns. The hidden value will hold the numerical only value of the row count while the visible parameter shows "XX entries". If you are adding rows via the backend, you will also have to update these values in the appropriate request details table. Then your display on the request and in the table display will show the correct values.
Additionally, if you see that the entries appear on the table component correctly from your backend procedure, you will need to clear cache related to the browser at the server level to show them in the application.
You can use kRunCacheManager.sh command, try doing this manually and if it works, then you will need to add that into the workflow to execute each time you have a procedure call to update the table component for new entries.