I found a tutorial which might not be up to date, but I could not find a better one.
It states several times:
This directory is then automatically encrypted when you log off.
Is this true? If yes, doesn't this mean that power loss can expose private data to someone who has physical access to the hard-drive?
It depends on how you set up the crypt (ecryptfs). If it is set up to automatically decrypt when you log in, then yes the data is decrypted when you log in.
This is the default behavior when you choose to encrypt home at login.
There are exceptions, depending on how you log in, for example, ssh and other methods do no not automatically decrypt home.
If you set up a private crypt, then of course if depends on how you configured it.
If you need a more specific answer, you need to tell us how you set upyour crypt.
I don't know what will happen with power loss and physical access.