To figure out why they are only seemingly alone, just look at the stage directions after Ferdinand's first lines in this scene.  It says "Enter Miranda, and Prospero unseen."  In other words, Miranda's there and can be seen, but Prospero cannot be seen.  Of course the audience can see him, but they understand that the characters cannot.

Miranda shows that she is tender-hearted by trying to get Ferdinand to stop working so hard.  She tells him that he can take a break because her dad won't be around for a while.  She even tells him that she'll carry the logs for him for awhile.