Color profiles are camera-model specific. You need to create a color profile for each camera. I’d guess you also have to give it an identical name for each camera, and maybe it isn’t even possible to synchronize across camera models even if you have the same profile name.
Yes you need to create a color profile for each camera, from a DNG image from each camera.
You can create multiple profiles for the same camera under different lighting conditions, and for different ISOs.
My Nikons have profiles-
"Sunny" is the "Camera specific" default for each camera, and "Shade" can be applied from the Camera Calibration panel if the images were taken in shade.
Before you make a Profile the Default for a camera (ALT+Reset = Set Default) , you can also adjust any sliders in the Develop module to your liking then save that as default. (eg. noise reduction for a specific ISO)
You could develop one identical image from each camera, develop them to look identical in "Compare View" then use each to save as a default profile. Ideally this will give a close match to the import appearance of photos taken by each camera at the same time.