Yeah ..... I'm not seeing a big issue there. As long as the insert is tight and doing it's job I don't see how a hole into the cavity matters much.Since the insert isn't protruding into the cavity it's really not a problem. Just fill the bottom of the hole with some wood filler. Next time measure the insert and put a piece of tape on the drill bit so you know when to stop.
the hole is inside the body in the cavity .... it's not visible.It's likely popping over the studs with no strings because you have the spring tension very high. I would also plug the hole you drilled through if it bugged me enough. And it might bug me enough. Just cut a thin piece of dowel, maybe 1/4" by 5/8" round (or whatever it is), and glue it in. The glued piece of dowel will hold much better than wood filler. You can use a little wood filler to blend the plug into the body. Paint it after, and no one will know.