Sometimes you get an alert from OEM but you can figure out why. It would help a lot if you could see the test and understand what exactly OEM is checking.
If this is the case, most (not all unfortunately) of the tests can be found as perl script on the agent side.
The directory location is (for 13.2 agent, it might be different for other versions):
<AGENT_BASE>/agent/agent_13.2.0.0.0/plugins/oracle.sysman.db.agent.plugin_13.2.2.0.0/scripts
Note that there is a directory tree under the scripts directory. For example, listener tests will be in the scripts directory. Most db specific tests will be located under the scripts/db directory. And Data Guard tests will be under scripts/db/dg directory.