There are many software products offering to watermark your images in batch without individually selecting the images. Is it common to use this kind of software or would photographers do it in Photoshop, manually, as needed?What are the advantages of using such paid tools
There are really two questions here:
Is it common to use software specifically for watermarking or better to do in Photoshop?
What are the advantages or task-specific tools?
I don't know any pros who are using any tools outside their normal workflow to accomplish watermarking. Maybe some people do, but Lightroom, Aperture, etc. have really made these tools somewhat irrelevant for photography and they are outside the normal workflow (more on this later).
In answer to the second question, the advantage would be that you could do a large batch of files without thinking about them. It seems appealing until you discover that you still have to look at the result for instances where the watermark was less than optimal (like in a cloud or over a shadow).
Most people are moving or have moved to a workflow that allows their main image processing tool -- Lightroom, Capture One, Aperture -- to apply the watermark to images exported with a given setting. That way, you start with the most resolution you have, create a watermark in a location that makes sense, and then say "export". Still in the same workflow.
And finally... someone once told me that "locks are for honest people." If someone really wants to steal your image, your watermark won't protect it, they'll just get creative with the clone tool. If you are looking to leave attribution on your image (that's what I do), then watermarking will work just fine.