Speed 'on conversion' means what it says to me. Maintain your Mach Number of choice until you or the FMC 'converts' to IAS and then fly at the IAS I have requested. If you are tight against someone else before reaching the 'conversion' level, then I will give you the IAS there and then with a 'when able' instruction.
Incidentally, the Mode S in our Centre gives aircraft Mach No. for the sectors operating generally above FL255 and IAS for those generally operating below. The sector groups operate on 2 different pieces of equipment.