Just tried it again with 1mb set at the limit file size. Same deal, 2 of the images were 1mb, the others were around 1.8mb.
Source images are all around 8mb.
What is the final megapixel count of the images? It may not be possible to make some of your images meet your size requirement if the images have a lot of detail, large ICC profiles, and large amounts of XMP metadata (Adobe Camera RAW settings can be huge!) given your minimum acceptable JPEG quality setting.
For instance if you have a 20 MP image and you set the minimum JPEG quality to 80 with Chrominance Subsampling on and you set the file size limit to 1MB it just isn't physically possible. You may have to set the quality down to 10 in order to get that size.
Take one of these images (that didn't meet your size earlier) and use Save As and turn off the Limit size checkbox. Now adjust the Quality slider until your image (with the same output settings as in the Upload dialog) achieves the size you desire. What is that JPEG Quality? It will likely be lower than your Minimum Quality from the Upload dialog.
Basically you can't have your cake (high Quality with large image) and eat it (low output size) too. It just can't be done. Try lowering your Minimum Quality more. Or crop/resize the image, or increase the file size limit.