I must of missed the memo . . . .

[Yulaldie]

In my experience, every island has either a bottle or furniture in a tree. Sometimes both.

 

[Dewasa]

DIY bottles is not 100%, the items from trees when visiting a mystery island is 100%, unless you're visiting one of the randoms like fruit tree island as items can only come from non fruit trees.

This has been my experience when visiting close to 150 islands.