I think copy works on pixels, while tint works on images. So they are not compatible.

Since copy basically is a combination of get, resize and display, you could do these seperately with tint.

Adapted Code

1. PImage img = loadImage("http://www.webdesign.org/img_articles/11441/_tinted.jpg");
2.  
3. void setup() {
4.   size(img.width, img.height*3);
5. }
6.  
7. void draw() {
8.   // original
9.   tint(255, 255, 255);
10.   image(img, 0, 0);
11.  
12.   tint(0, 0, 255);
13.   // copy (tint doesn't work)
14.   copy(img,img.width/4,img.height/4,img.width/2,img.height/2,0,img.height,img.width,img.height);
15.   // get
16.   PImage segment = img.get(img.width/4,img.height/4,img.width/2,img.height/2);
17.   // resize
18.   segment.resize(img.width,img.height);
19.   // display (tint does work)
20.   image(segment, 0, img.height*2);
21. }