(This is for ACR - Adobe Camera Raw, and Photoshop only. I don't work in LR, so I don't know how to change it other than you need to change it for export)
Ok, so let's talk just for a quick moment on how to change the colorspace and why you want to do it. It's actually very simple. So, first you are probably wondering what colorspace is, I really don't feel like getting too far into that, so I will just give you a very basic rundown. The thing is this, ProPhoto is the largest space, Adobe RGB is second and the third, and smallest, space is sRGB. You can only take the photos in two colorspaces and that is the Adobe RGB or the sRGB.
When you take the images you should record them with the most color data you can possibly get, kinda the same reason we shoot in RAW, for the most data possible. Set your camera to Adobe RGB and then it comes time to work in sRGB and that is what is used for web and most print. The reason you shoot higher colorspace is so that should you ever need that color data and need to print with CMYK and ProPhoto (massive editorial stuff) you will have that data available to do. For everything else, sRGB is what is most widely used and accepted.
So, here we go. I have some screenshots to help show you right where to make the changes upon import and finally into Photoshop.
1. Below the image is a link, do you see where it is in the center in the same row area as the "open image, cancel, and done?" It says sRGb.......and some other stuff? CLICK THAT!!
2. A text box will now open, and this is where you change the colorspace to embed as sRGB. Make your selection and click OK.
3. The next step would be to choose OPEN IMAGE. You HAVE to open the image to basically complete the path and get it to stick. Once you do this and the image opens in Photoshop, you will set the change and not need to do this again.
4. Once you are inside of Photoshop, you will want to select EDIT.
5. Select Color Settings......
6. Here will give you the color settings box, you will choose the sRGB option in the RGB box.
7. Select the sRGB.
8. Now, if you are on a PC (non-mac) you will choose Gray Gamma 2.2 for the third box (under CMYK).
9. And....if you are on a MAC, you will choose the Dot Gain 20%
So, there you have it. Click OK. Now you are shooting in the largest colorspace you can record in the camera to have the most data, you are sRGB embedded, and sRGB working and saving colorspace. This will ensure uniformity across the board. IF you are still noticing color variance when you post, please be sure that you are calibrated (with an actual calibrator, not something you can just do in settings).