Photoshop cropping variable images

What you mean by "cropped"? Can you post screenshot of Variables dialogue where variable is defined. 

Depending on image dimensions you may see entire image or only fraction of your image when As Is is chosen for fitting option. Do you understand what each of fitting option is doing? There are and some other important options as explained below.

Beside option to choose fitting method there are option to set Alignment and Clip to Bounding Box. Do you understand what those options are doing to placed image?

Alignment: when center is set that is instructing Photoshop to align center of image to center of rectangle with variable assigned. When top left is set that is instructing Photoshop to align top left of the image to top left of rectangle.....

Clip to Bounding Box is instructing Photoshop to delete pixels outside of rectangle or shape with assigned variable, that will effectively crop pixels sometimes what depend on method and image dimensions.

Here is my tutorial that is trying to explain fitting and alignment options with alternative to Clip to Bounding Box Easy Way to Automate Photoshop with Variables (Part 6) | DezignEasy

Fill is going to fill the shape while keeping the proportions, so if the proportions are different from the shape, then the image will be cropped.

You might try Fit instead, or check that your images are the right proportion if you continue to use Fill.