A Honeywell document states the following regarding TPE331 engine starting:
CAUTION
DO NOT ALLOW THE ENGINE RPM TO “DWELL”
BETWEEN 18 AND 28 PERCENT RPM. IF NORMAL ENGINE
ACCELERATION WITHIN CRITICAL SPEED RANGE
DOES NOT OCCUR OR IF THE RPM STOPS INCREASING
PRIOR TO REACHING NORMAL IDLE, “ABORT THE
START”. (Refer to AFM/POH)
This passage is found in the section regarding air starts:
- It is important not to allow the engine to windmill between 18% to 28% RPM (shaft critical RPM) on TPE331-1 through -12 or between 14% to 20% RPM on TPE331-14/-15 engines.
CAUTION
CONTINUOUS OPERATION/WINDMILLING WITHIN THE
SHAFT CRITICAL RPM RANGE MAY CAUSE ENGINE
DAMAGE.
Thus the limitation apparently applies for all modes of operation. The mention of a 'critical speed range' and 'shaft critical RPM' indicates the issue is likely related to resonance.
http://eastaire.us/files/TPE331pilotnotes.pdf