Exchange 2013 Office 365 Hybrid Password Changes

We have recently rolled out our Exchange 2013 Hybrid with Office 365. We're using ADFS with Azure AD DirSync and Password Writeback is enabled via the HCW tool. The Azure AD Sync runs at the minimum setting of 30 minutes.

My question is just getting clarification on passwords and syncing as I can't seem to find a concrete answer.

1. If a user reset their password On-Premise, does it immediately push out the new password to Office 365? Or does it wait until the next password sync comes via the Azure AD Sync tool?
2. If a user resets their password in Office 365, does It immediately push it back to On-Premise? Or does it wait until the next password sync comes via the Azure AD Sync writeback function?
3. If a user locks themselves out On-Premise, I would image that it wouldn't lock them out in Office until the next AD DirSync