Maybe it's me. But I don't understand what you are asking. The spring has to fit in the barrel. Measure your barrel and the spring has to fit below the lip of the cap. Length is important and the thickness. Did you receive a barrel without a spring?
I've come across a couple of clocks that have popped barrel caps because the spring height was too much. If I've changed the springs that have popped the cap or put springs in where they were missing altogether I leave 1mm tolerance for the spring to move freely. I don't know if this is the technically correct tolerance or not but it seems reasonable to me and not had a problem...yet.
You don't want a lot of room for the spring to move laterally in the barrel. That can pop the cap off. If the spring fits just below the lip, you should be fine. I'm sure there is room for tolerance, but all of the factory supplied springs I've come across have a pretty close fit.
shutterbug is correct,many times you will see wear marks on the inside of the cap,i have never heard of a depth tolerance for spring barrels,spring should be just below the the cap recess,some times you may need to stake the cap to the barrel edge as i have seen many barrels oversized and beat up because repairer didn't know how to install the cap correctly,some think a hammer and punch are needed??most caps are slightly over sized and designed to snap or pop into the barrel recess,i use a set of soft jawed slip joint pliers