First of all: Why are you using EPS? Don't! Use PDF/X-4 or AI instead.
There is no need to open a placed file with a wrong spot color in InDesign. Open the ink manager and target the wrong spot color to the correct one.
The appearance of a spot color on screen should not bother you as the printer will print it with the specific ink.
Did you check the overprint preview and high quality display in InDesign?
How does it look like, if you export to PDF/X-4?
Thanks for your reply Willi. Why do you advise not using EPS? This was just how the image had originally been set up.
When I exported the document to PDF, there was no colour variation. Also, there was no variation when actually printing. Fingers crossed it will all stay like this! Why would there be such a difference in the InDesign file, but then it exports and prints ok?
EPS is an old and outdated file type as it does neither support color management nor transparency. It has been replaced by PDF and AI. It is recommended not to use postscript at all with InDesign.
Ok, thanks for letting me know