Batch processing of PSD's to sRGB. Need help.

Thank you so much. The image you shared was quite helpful. I was utilizing File Info to check the status of the profile.  (I resolved the problem eventually by changing the Working RGB space in the color settings box.). My files all show a color space as "RGB" and a profile as "Adobe RGB" (or sRGB for the jpegs.) My color settings show Adobe RGB. Where does this color space become defined?

Next, I am the photoshop idiot of the month. (Hopefully my identity will stay reasonably confidential, so please do not mock me), but I completely forgot that I was doing color correction for my images on an imac screen that I had set, in system preferences, with a home-cooked calibrated setting. It is easier on my eyes for it to be warmer and I FORGOT to change it to the Adobe RGB option.  The images look good despite, but obviously cooler than I would have made them, quite a large error.  With this in mind, please can you advise, when editing, should I have my monitor set to Adobe RGB, since I will be working with this profile for printing? Next, the TIFF's that I created to send to my client (with LZW compression) shifted and became much cooler (skin tone) than my original PSD files.  However, the jpegs I created, with sRGB looked much better/closer to the PSD's.  Thank you for your expertise. 

Thank you to everyone for the helpful replies.  I was finally able to resolve it by tinkering with the Color Settings, I changed the Working Spaces RGB setting, I cannot recall now what it previously was. It is now Adobe RGB (1998).  Then I re-recorded the Action and ran it through Automate-batch. It then converted the PSD's to jpegs and sRGB as I directed. However, I still have confusion over some color profile issues. The TIFFs I created for my client to print files from, I compressed with LZW in order to email them. When I viewed these files, there was a noticeable skin tone color shift from the PSD files which were also using Adobe RGB. However, the Jpegs look similar to the PSD's!  I wanted the images to resemble my PSD's for printing, is it the LZW which shifted the color or the TIFF's? (Why do my PSD's say RGB as the "Color Space" and profile as Adobe RGB, is my "Space" correct?) Also,

what is "without dither" referring to? I ran my files "with dither" because I didn't understand the option.  And, why did you not check the box to convert to sRGB, rather than running the Action in category 4 of the Preferences for the Image Processor?  Is there a benefit to using the Action? I also used the Relative Colormetric setting , but was advised by someone that using Perceptual was better.  Thank you for your expertise, so much appreciated.