First Officer reported loss of Cabin Pressure Control while in cruise. The flight crew made an immediate descent and was able to clear the CAS messages. The flight diverted and made a precautionary landing.

Narrative

Enroute from ZZZ to ZZZ1 on an empty ferry flight; I was Pilot Flying in the right seat as SIC and Name was Pilot Motioning in the left as PIC. We needed to climb to FL450 to get above weather. Shortly after leveling off and pulling thrust levers to cruise; we felt a large 'woosh' of air followed immediately by 2 CAS messages (ACM OVER TEMP and Emergency Pressurization). The PIC called for oxygen masks on and immediately [requested priority handling] to ATC and asked for lowest altitude possible. ATC cleared us to FL340 initially and we began a [priority] descent with spoilers deployed in FLC. In the descent we ran the QRH while ATC cleared us to 15;000 ft. Upon descending out of FL210 and completing the QRH; both CAS messages were cleared. The PIC told ATC we no longer needed to be declared as a priority aircraft as the situation had been resolved; but we would like to divert for a precautionary landing. ZZZ2 was the nearest suitable landing field; and we made a normal approach to landing.