Ok, so the edits you accomplish in Lightroom are non destructive. this includes metadata edits. Not sure what metadata you are editing (tags?) but that data does not get written into the image file. That data is in the Lightroom catalog (a database) for use in Lightroom to go with that image file.
This is true for develop edits, library metadata edits, keywords, labels, flags, etc.
Now, if you turn on Automatic write changes into xmp (in the catalog settings for metadata) a sidecar file gets written, that can provide that info to external programs that are xmp capable. I have no idea if finder is, but this is off by default.
Be aware, that if you are editing DNG files, and Automatically write changes into xmp, then that data is written into the DNG (if it is a DNG created via LR)
So, normally, that image file, contains no info about any changes you accomplish in LR. And any changes you did in LR will not show up.
Now, if on the other hand you export a file,and do not tell LR to strip any metadata (look down towards the bottom of the export dialog), then those edits should get baked into the new file.
To experiment, select a image that you imported from your camera, be it RAW or JPEG. Go into the develop module, realy really up the exposure, make it ugly. Minimize LR, bring up fider, navigate to the image, see what you get. Oh, and notice the modified date, probably no change.