Does this is an aggregate initialization or reference initialization?
A is an aggregate and A a{ B() } is list initialization according to the following rule(s):
The effects of list-list-initialization of an object of type T are:
- If - Tis an aggregate class and the braced-init-list has a single element of the same or derived type (possibly cv-qualified), the object is initialized from that element (by copy-initialization for copy-list-initialization, or by direct-initialization for direct-list-initialization).
 
- Otherwise, if T is a character array and the braced-init-list has a single element that is an appropriately-typed string literal, the array is initialized from the string literal as usual. 
- Otherwise, if T is an aggregate type, aggregate initialization is performed. 
(emphasis mine)
Note in the above, we do not reach bullet 3 as bullet 1 is satisfied and so used.
This means that the object A is initialized from the single element B() using direct-initialization. This in turn means that the copy constructor A::A(const A&) will be used.
Here, the parameter const A& of the copy ctor A::A(const A&) can be bound to a B object so this works without any problem.
why this is not an aggregate initialization even though the class A is an aggregate class?
Because to do aggregate initialization bullet 3 here should be reached and satisfied but we never reach bullet 3 because bullet 1 is satisfied.