It is not actually Hangfire, it’s just static fields are initialized when the type is referenced for the first time.
You may want to make
myCache lazy (so it would be loaded only when it is actually accessed, instead of when the type is loaded):
private static readonly Lazy<SomeData> myCache = new Lazy<SomeData>(LoadValuesFromDb);
Type initializers are executed once per AppDomain, so if your Hangfire server runs in the same AppDomain as client, the cache will be loaded just once.