This has everything to do with how shape objects are created before hand.
You can read my tutorial on the subject here:
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www.kenstone.net]
Once you understand shapes, you have to dig a little deeper to see what is causing this issue for you.
First, in the shape object itself, there is a mask layer which defines where the picture asset you are dropping will go. The dimension of the entire shape object is 100% and your image will define itself to that scale based on the x and y. So as an example, if in my shape object I have a frame boarder, then because that frame consumes the surrounding area of total x and y dimension, some of my image I drop into that drop zone, will be cut off by the shape layer, which overlays the mask layer of the button or drop zone shape object asset. You will have to compensate for that by adding a border to the image you drop into the shape object to compensate for the shape layer that is covering up some of the image you dropped in.
Let me try to be very clear.
You have 4 clear plastic sheets. The are each 5" x 5" for the x and y.
One sheet, the bottom one, is a mask layer. One is a shape layer. The shape layer is what the drop zone or button looks like. It is the icon itself. Like a real picture frame you drop a physical picture into. Part of the frame of a picture frame covers a picture you fit between the glass and the backing of the frame. Drop Zones and Button shapes objects work this way. The shape layer covers the mask layer. Your image is fitted as best it can be to the 5 x 5 x and y, but the shape layer covers it a bit around the edges unless the shape layer is blank.
So your job is to make your image a little smaller so that it fits the glass area only, and not the full 5 x 5 x and y. So around your own image, you can add a bit more space. For example, make your image 4 x 4 and drop it on a photoshop background of 5 x 5. Now it is 5 x 5 but the part you want to see is 4 x 4. If the frame itself is 1" on all sides, you are perfect.
So there is compensation to be considered.
Read the article about shapes and you will understand their structure. Once you have that clear, you can create your own and perfect the results.
Now, if your shape is larger than the asset you drop it into, you can pan your image around in the shape by holding down Option-Shift and then dragging the image around. You can't resize it that I know of.