This is a very strange, but not completely unusual problem. I saw first in a 206 that Bell Helicopter had as a taxi between facilities. The engine was glacial in spool up from 48 to 62%- it would actually stop accelerating when the starter switch was let off, and needed the starter to re-accelerate to idle.
Next saw something similar on an OH-58C. Exactly the same symptoms you describe. Cold start is very slow from 45-62%, warm start OK.
Talk to an Rolls Royce rep - it's something in the fuel control - either a diaphragm that's got a hole in it, or something else leaking in the fuel control.
Definitely not normal, and someone in Rolls should know how to fix it.