When not using (C)DI, you can easily see when a component is created too early by looking at the stacktrace:

"database username is null"
at ConnectionManager.createConnection()
at DogDao.createInstance()
at DogDao.getInstance()
at PersonDao.createInstance()
at PersonDao.getInstance()
at PersonService.createInstance()
at PersonService.getInstance()
at Main.beforeDatabaseUsernameIsAsked()

Clearly, beforeDatabaseUsernameIsAsked() has the problem: it shouldn't call PersonService.getInstance().

However, turn this code into (C)DI and you get something like this stacktrace:

"database username is null"
at ConnectionManager.createConnection()
at java.reflect....
at org.jboss.weld...
at org.jboss.arquillian...

Now, it's not clear any more that Main.beforeDatabaseUsernameIsAsked() is the problem, isn't it?
There is absolutely no mention of Main.
And then it is a challenge to find out what's causing the lifecycle to behave differently that you expected
and how the lifecycle is actually behaving now.

It would be nice if the exception message contains something like

"database username is null"
  during creation of ConnectionManager
  for DogDao
  for PersonDao
  for PersonService
  for Main
at ConnectionManager.createConnection()
....