When you create an object with new, you are responsible for calling delete. When you create an object with make_shared, the resulting shared_ptr is responsible for keeping count and calling delete when the use count goes to zero.
Going out of scope does mean leaving a block. This is when the destructor is called, assuming that the object was not allocated with new (i.e. it is a stack object).
About the only time when you need to call a destructor explicitly is when you allocate the object with a placement new.