The borders of the post-Allied victory Germany had already been agreed at the Yalta conference in February 1945. So the purple area on your map is where the US army had moved into what had already been agreed to be the Russian zone. This occurred partly because the German Army put up less resistance to the British and Americans than to the Soviets- not surprising considering the Red Army's treatment of German civilians and POWs.

In fact, the British and Americans could have got to Berlin before the Russians did. The British 2nd Army was only 3 days away, and the US 9th Army was also close. However, Allied command decided it would not have been worth the casualties of taking Berlin and its surrounding suburbs if it was just going to be handed over to the Russians anyway.

Armageddon by Max Hastings

Storm of War by Andrew Roberts