You are likely not using a kerf adjustment or using it incorrectly to compensate for laser beam cut size.
Figure out the kerf and they apply 1/2 of the kerf to the object. That moves the tool path out to correct for the kerf.
If the material heats up too much, melts… you need to figure different speed/power to make that the minimum.
It’s a fiddly job to get it set up properly. I know you know what’s happening, but with no settings you’re using, not sure what to tell you…