Assuming what you're cutting out is the "Hilltop Ruins" model that
oldschooldm did cutfiles for over on the Fat Dragon forum... I just downloaded the cutfiles and that looks like "Hill 2.pdf". I copied the image out of the pdf, and merged into the cutfiles, and they DO definitely align.
Try this:
Open the PDF page in Acrobat Reader.
Ctrl+0 to zoom so the full page is in view.
Edit > Preferences menu -- in the General section ensure that "Use fixed resolution for Snapshot tool images:" is checked, and set to 300 pixels/inch.
Edit > Take a Snapshot menu
Single click on the page. It should blink and make a "ding" sound.
Open the "Hill 2.studio" file.
Ctrl+V to paste the image into it.
Click on the image, then use the Scale tool to change the dimensions of the image to Width: 8, Height: 10.5
Ctrl+Shift+[ to send the image back behind all the cut lines.
Use the arrow keys, and the image should line up with the cutlines.
Side note - hopefully the score lines still work as score lines. The newer versions of Silhouette Studio don't let you make perforation lines anymore. You instead make dashed cutlines. So, you might want to select the lines that are supposed to score and change their line style to be a dashed line, and change their cut style to cut.