You are probably multiplying a color on top of an image in Illustrator, right? Or maybe you a re doing it some other way.
The problem is that when you export a pdf to print using a color profile which should only allow a total ink of 320%, Illustrator (or other applications like InDesign) doesn't analyze your layers in depth to make sure that your layered artwork actually complies to the color profile. It simply converts each object separately, so your image gets a total ink of 320%, but then you add more color on top resulting in too high total ink.
So, what can be done about this? I have two different approaches:
Add the color tint to the image in Photoshop in RGB and convert the image to the correct CMYK profile (you probably do this on export in Illustrator). This way the colors will be converted as a whole and the total ink of the color profile will be honored.
It looks like you are adding a green on top of a neutral image. If you are using an RGB image it will consist of all four CMYK colors when converted to CMYK. If you convert your neutral image to grayscale you have made sure that the resulting color never can get any darker than your green color + 100% black. Depending on the green color, this will probably keep you below 320%.