Hi J
Yes that's right, the tension of the spring keeps it on. So when you come to fit it, there will be stretching needed on the spring to fit it to the center stand, sometimes not an easy job depending on how tight the spring is so be careful of your fingers.
The way I have always done it is fit the hook on the frame, fit the spring to the hook (making sure the loop on the end of the spring is at the correct angle to fit over the center stand retainng bit, have someone hold the bike over a bit on the offside, push the center stand up so there will be least tension on the spring, slide a screwdriver on the spring end loop and on the center stand retainng bit and then force the spring end loop over the retaining bit.
Hope this helps
Cheers
T_revs