The game autosaves after you've sailed to a new island, not every time you visit the island's "main screen". You can still save manually in each "Savespot". (This is because the size of the game - as you've probably noticed, saving takes a lot of time, and I didn't want to introduce this long pause every time a player goes back to the island's main screen). Basically, whenever an autosave gets recorded, you get a "Game saved automatically!" message at the top of the page, and Savespot means you can save manually. Sometimes both happen at once.
Glad I could help, and good luck with the rest of your run!