SQLITE and autoindexing
SQLite requires an index to enforce the PRIMARY KEY constraint -- without an index, enforcing the constraint would slow dramatically as the table grows in size. Constraints and indexes are not identical, but I don't know of any relational database that does not automatically create an index to enforce primary keys. So yes, this is normal behavior for any relational database.
If the purpose of creating an index is to optimize searches where you have an indexable search term that involves the first column in the index then there's no reason to create an additional index on the column(s) -- SQLite will use the automatically created one.
If your searches will involve the second column in the index without including an indexable term for the first column you will need to create your index. Neither SQLite (nor any other relational database I know of) can use composite indexes to optimize filtering when the head columns of the index are not specified in the search.