Is it possible to route ingress controller traffic to different services/deployments based upon the file type in the path?

No in that way. You would need to route your request to NGINX which will send request for *.php to a PHP_FPM. You can have that as separate Containers inside one Pod or as Services. Service example is nicely explained in How To Deploy a PHP Application with Kubernetes on Ubuntu 16.04

In this example you will have two containers NIGNX and PHP_FPM running on the Pod. PHP-FPM will handle dynamic PHP processing, and the NGINX will act as a web server.

You will need to use custom nginx.conf configuration and in my opinion the easiest way would be using ConfigMap.

Your ConfigMap might look like the following:

apiVersion: v1
kind: ConfigMap
metadata:
  name: nginx-config
data:
  config : |
    server {
      index index.php index.html;
      error_log  /var/log/nginx/error.log;
      access_log /var/log/nginx/access.log;
      root /;

      location / {
          try_files $uri $uri/ /index.php?$query_string;
      }

      location ~ \.php$ {
          try_files $uri =404;
          fastcgi_split_path_info ^(.+\.php)(/.+)$;
          fastcgi_pass 127.0.0.1:9000;
          fastcgi_index index.php;
          include fastcgi_params;
          fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
          fastcgi_param PATH_INFO $fastcgi_path_info;
        }
    }

Nginx will catch and send all *.php request via localhost:9000 to PHP-FPM container.

You can include the ConfigMap in your POD using the following:

apiVersion: v1
kind: Pod
metadata:
  name: nginx
spec:
  containers:
    - name: nginx-container
      image: nginx:1.7.9
      volumeMounts:
      - name: config-volume
        mountPath: /etc/nginx/nginx.conf
        subPath: nginx.conf
  volumes:
    - name: config-volume
      configMap:
        name: nginx-config
  restartPolicy: Never