Is Spotlight index on an external USB drive reused when connected to a different Mac?
Every time you connect your drive to a different computer it gets indexed on the computer. Since your drive is 10TB indexing can take quite a while regarding how much data stored on it. I would suggest to deactivate indexation in the Spotlight options (indexing slows the computer down) but I noticed that un mounting/mounting the device to your/a computer erases the parameter in Spotlight so indexation is back on for the drive!  (on my system)
I hope this answers your question. 

==> I forgot to mention that I have to delete all the 'fancy' dirs that macOS creates on my external drives to avoid issues when I connect these external drives to my DJ equipment.
I learned the hard way that if I don't remove those dirs, that it possibly will brake my ext. drive! (lost 2x 3 TB hard drives with tons and tons of music on it. The issue is known by the producer of the equipment but they aren't going to change a thing about it. For Denon, it's a macOS issue and not a Denon issue. :-( )