I don't get any warnings when opening in Photoshop. Here's an example of a raw file, no adjustments done in LR, and opened in PS. PS is much darker and more saturated. I just recalibrated my monitor before creating this screenshot. If I export the raw file as a .tif or .psd, it looks identical to the raw file in PS.
If those truly are screen shots taken while first bringing up the same RAW photo into the two programs, with no manipulation of the image yet applied, it could be the automatic application of some processing as it is brought in. Some programs attempt to mimic the camera's settings at the time of shooting, others don't, if I understand on difference correctly. Also, the programs can be set up to apply a predetermined set of parameters which are independent from camera settings at shot time...I could have LR apply one during auto Import vs. a different one during manual import. You might not be seeing rendition differences in monitor profile!



