I am new to Photoshop CS6. My edited photos look much more saturated on phone screens than they do on laptops. One of the pictures that seemed relatively blue on the laptop screen appeared to have a greenish tint on phone screens. I have tried assigning the colour profile to sRGB. Didn't quite cut it. I even tried 'Flatten Image to Preserve Appearance' and that was in vain, too. How do I fix this? Thanks in advance.
If the devices you are checking on are not colour-profiled then there is not a lot you can do. Any image is going to look different on each.
The best you can do is ensure that it leaves your machine in the best possible way.
This assumes your monitor is already calibrated & the profile is available to your OS.
Make sure Photoshop is set to the correct RGB profile to start with - Edit menu > Colour Settings. If you are outputting mainly to random screens or the web, then sRGB is the 'safest' bet. Most un-calibrated screens at least nod in the general direction of sRGB from the factory - though whether it's a deep bow or really just a tip of the hat is dependant on far too many factors.
Photoshop should know to not touch the profile at import from your camera - Colour Management should all be set to 'Preserve'; your workspace should be set to sRGB.
Your monitor profile needs to show in the list for Workflow, but should not be selected as RGB profile. The colour adaptation for your monitor profile is done 'live' to the screen so isn't part of your workflow.
Rather than reduce the potential quality of your master image, once you have done your necessary work, then use the Export panel - Edit > Export > Export as...
Set your format, size, quality if .jpg in there & check 'Convert to sRGB' - that is the only point at which the picture's profile is updated.
One conversion, at output.
[You can embed the sRGB profile if you like, but many apps/browswers discard it & assume sRGB anyway]
All you can do then is hope - that whoever views your image has a screen that's at least somewhere close to sRGB.
How to make sure that photos edited in Photoshop CS6 don't look different (more saturated) on phones
Don't look at them on most phones. The screens on most phones are too bright, too saturated, and too blue (calibrated to around 7000K).