This has been a bugaboo of Photoshop since they first started reading JPG files. Adobe is all about quality, and the "lossy" nature of JPG format chafes them. True JPG theory dictates that every image is unique, and should be considered individually for JPG compression, due to loss, size of file, etc. Batch processing the saving of JPGs besed upon global settings for Quality or File Size is unacceptable to Adobe. When PS creates or manipulates an image and saves it in JPG, it "tags" the JPG with the compression settings chosen for that image. That's why when PS says "Saved" images, it means previously saved by using PS. That way, it can reuse the original compression settings embedded in the file. Folders don't matter, Save vs. Save As doesn't matter....if it's a JPG, and if PS didn't make it or manipulate it, it's going to prompt for a compression setting....no way around it.
Solution? For most, it involves never using PS to batch process JPGs. Convert to TIF or BMP as a first step, to minimize loss, make all PS changes to these files, then use another program to batch convert back to JPG (ACDSee, Thumbs+, SuperJPG, etc.). That's my large-quantity solution. I created an action to resize to 800V, then save as TIF and Close - and another for 800H. This allows me to get everything used in mass quantities at web size, then run any other actions on them as needed, batch by batch. I've still got the originals, of course, for those "sorted" pics that require full-size care for printing.
Why resize before saving to TIF? Easy, because TIF conversions of my Fuji S2 Fine 6MP JPGs creates either a 7.4MB compressed TIF or a 17.4MB uncompressed TIF. 12MP mode, double those sizes. After resizing to 800 long side, it's just 1.22 MB uncompressed for the 6MP! MUCH faster for PS to work with.