Why don't I don't see any metrics under database tab ?

You might have disabled SQL Query listening in your Agent. Enable it by setting true for the below key.

Name	Key	Description	Default value
Capture Database SQL Queries	sql.capture.enabled	Enabling this option will help listen to all the SQL Queries that get executed. If it is disabled, no Database Metrics will be collected.	True

To access the Enable option go to Settings → Discovery & Data Collection → APM Insight Agent Configuration Profile → <Your-APM-Insight-Monitors-Associated-profile>

Check if the database used is supported for respective agents.
Check if you are using any wrapper around the JDBC client and if the database calls are initiated from the same application server where the APM Insight agent is installed.