So it's far from fully automatic. There's a lot of work done on the tools, but there are also a lot of additional constraints to deal with with each new nodes. It's a real complexity explosion, and this is what makes designs on advanced nodes so much more expensive. This a highly simplified description but hopefully enough to get a feeling for what's going on.
Depending on the complexity of the chip, the backend process takes several months. It's an iterative process. A reasonable complex chip has to be split into several partitions. The size of the partition determines the turn around. In the designs that I have worked on, we try to limit the turnaround time (RTL->GDS) to be one week for the larger partitions.
I would change your statement to say that the EDA vendors have created tools that allow Physical Design engineers to address the design challenges. It is still a gruelling, iterative, painstaking process.