I think this metaphor is also meant to evoke the Black Mary, which we learn about in Chapter 4 of The Secret Life of Bees, in the same scene in which Lily and Rosaleen first meet May. Black Mary is a figure that is "black as she could be" (70). She has "a faded red heart painted on her breast" (70) and "a candle inside a tall red glass threw glints and glimmers across her body" (70). The statue's impact upon Lily is profound, "so big it ached like a moon had entered my chest and filled it up" (70).  May, of course, is black, as well, with "palms pink like the bottoms of her feet" (71), which fills Lily with "tenderness" (71). 

Black Mary and May, with their contrasting blacks and shades of red, have a strong and positive impact upon Lily, the Black Mary seeming to confer some serenity and protection upon her, and May making her feel very protective.  I do not think the metaphor later on in the book is a coincidence at all.  We are meant to remember that Black Mary's heart is on her outside, providing strength and hope, while May's heart, on her inside, makes her vulnerable. 

May sank down onto the floor, crying and looking so hurt inside I could almost see soft, red places up under her rib bones.

May is one of the most sympathetic and compassionate characters in the book.  When others are sad, she is sad.  When others hurt, she hurts with them.  She is so sensitive, in fact, that she physically experiences emotional pain, even when it is the pain of others.

The metaphor here paints a vivid image of the physical way that May embodies emotional pain.  Here, June is fighting with Neil, and May is the one who reacts the most.  Lily imagines May's heart burning so brightly that it shows red through her ribs and skin.