edit: One note about something that was bugging me for a while...items created on my computer sometimes wouldn't show up in the vault for immediate use. Painful when you sign up for a service using your computer and then try to immediately sign into it on your phone.
In the iOS app settings there is 'Swipe down to refresh' (or similar) - turn that ON. Not sure why it was off by default, but it totally fixes the issue. Just swipe down to refresh the vault and your new item appears.