I have set up two reports, source and target to test cross report drill through. It works fine in the power bi service, but not when the report is being embedded (Apps own data).
Is this a limitation or am I missing anything? Is there a workaround?
Not, it doesn't work. When you embed a report, you specify which report exactly to be embedded. The cross-report drill through will try to open another report (not the one, which is embedded), which isn't a problem in a browser or Power BI Desktop, but this will not work when embedding. You can try to combine both reports into one, on separate pages, as a workaround for this issue.
You can vote for this feature here - Enable cross-report drillthroughs for Power BI embedded.