are there any tests i can debug to understand entire flow when a user fires a insert command involving timestamp?

If you just wanna focus on the statement parser then check:

org.apache.pinot.sql.parsers.CalciteSqlCompilerTest

Or if you wanna the whole e2e, try to run this:

org.apache.pinot.integration.tests.SegmentGenerationMinionClusterIntegrationTest

I am working on issue to add support for timezone, so want to understand e2e working of timestamp.