disclaimer: when in doubt read the manual
Just to add some background.
Typical multispool by-pass Engines have a nasty effect on precipitation when operating at low power (taxi on the ground, descent and approach and yes even at crusie). They depress the temperature of the ingested airstream in the front section of the engine, (inlets, fan, and yes even the front spool stages of the compressor) This of course makes much more likely that the engine will acrete ice somewhere before the aircraft does at these conditions.
Most engines are tested to handle the acretion and shedding cycles of ice in actual flight operations as long as you are at or above flight idle. However engines are not tested to handle icing at ground idle conditions or at depressed idle conditions in the air.
And the of course there are the ringers where even in cruise the engines may acrete enough ice over time behind the fan in the front compressor spool which when shed may cause some serious surprises. These type of problems are often what are addressed by subsequent airworthiness directives aimed at operating condition avoidance.
As far as different procedures for different engines. This has a tendancy to get combined with rumor and compound misunderstanding of ice and the powerplant. As such all the engine and airframe manufacturers were urged to maintain the same wording in their operating manuals relative to the conditions of when to expect icing. I haven't personallly reviewed all the various manufacturer's manuals, but I would be disappointed if there was any variance between engines in this regard. Of course what get's rewitten later by individual operators is another story.