What you are describing is a Print and Cut file…it’s not something the laser is designed to handle without a jig at the moment. (Although one day, I’m hoping they will get the visual alignment with the camera squared away enough to use it that way.)
If you want to use it that way now you are going to either need to create a jig for your cards, or use indexing marks of some kind on it.
The jig is quicker, but when inkjet printers print on paper products, the image can be shifted quite a bit because of variances in how the paper gets fed through the machine - the feed tray guides can be a little loose in most cases so you rarely hit the actual printing in the same place twice.
This is what is causing some of the variances. There’s nothing tying where it’s printed on the paper to the cutting and scoring lines you’ve created, and visual alignment isn’t close enough yet.
There is a tutorial for creating indexing marks on your paper and using those to align the print with the cuts and scores here:
That’s one of the methods we use to make the laser do a Print and Cut file. 