The Visitor’s Blue-Eye Announcement

On an island live perfect logicians. Each person can see everyone else’s eye colour but cannot see their own, and nobody may discuss eye colours. Every islander knows these rules and knows that everyone reasons flawlessly. A law requires anyone who becomes certain of their own eye colour to leave on the ferry that night. Before a visitor arrives, no islander has ever publicly confirmed that anyone has blue eyes. The visitor gathers the entire population and announces, truthfully, “I can see at least one person with blue eyes.” Everyone hears the statement and knows that everyone else heard it too. In fact, exactly five islanders have blue eyes. Assuming the announcement is made during the day, after which night do the blue-eyed islanders leave?