But your colourist would have to re-export the clips adding a gamma tag and a colour space tag to the clips in the Resolve deliver page. If this is too much of a hassle, you might as well adjust the clips yourself for this project and set things up properly for the next one.
Well, it turned out that a simple correction is FCP wasn't that simple. In the end I had to go into Resolve, but after hours of trial and error, I found the suitable settings.
In the project settings, despite what I read online, setting the gamma to 2.4 didn't solve the issue when exporting into other programmes.
I found that in the Colour management settings if I set it to rec709, gamma 2.6 however, then the image remained consistent through all the programmes. Unfortunately setting it at 2.6 also shafted hue and saturation from the intended grade.
The work around turned out to be simple to counteract this. I applied a colour space transform note, with my gamma input settings at 2.4, and my gamma output settings at 2.5.