The timing of the traffic being issued to AEM needs to be put in context. The En-Route ATC has very little time to issue the traffic statement from when it's transferred from Departures. The aircraft is transitioning from CTA, obtaining weather information whilst still in CTA, briefing the approach whilst in CTA etc, etc. It then changes frequency to Centre, then changes to the CTAF. It's a very high workload, let alone it being a training flight.