The medulla gets the blood before the cortex in our circulatory system.
Actually, in more technical terms, the circulatory system supplies the blood to both the cortex and medulla at the same time. However, the common carotid artery that supplies the blood to our head or brain reaches the medulla before it does the cortex. The actual time difference between the reception of blood in the medulla and the cortex is probably on the order of milliseconds. The cortex takes much longer to get vascularized as compared to the medulla. Also, the vertebral arteries (a branch of the subclavian artery that have a much more direct route than the carotid artery) also supply the blood to the medulla. Thus, the medulla receives the blood supply before the cortex.
Hope this helps.