PC-12 pilot reported cabin pressurization malfunction during departure climb. Pilot descended and diverted to a nearby airport.

Narrative

Leaving ZZZ filed IFR to ZZZ1 we were climbing to 19000. at 17000 I had an ECS fault and jumped into the QRH. I began a decent and exercised emergency authority. I asked ATC for lower while I went through my check list. I should have declared right then. I let the crew know what the status was as much as I could while going through the checklist. Then I had an ACS Low Flow fault. and descended to 10000 at a rate of 2000' per min. cabin pressure was about 6000' and rising at a rate of 1500'. I should have turned on oxygen to be extra safe and should have [requested priory handling] as I was exercising emergency authority before I received clearance from ATC. As cabin pressure was on the rise we(crew) discussed the current cabin alt and our oxygen status. As I passed through 11000 our cabin alt came up to 10000 and gave us a separate Warning cas. at 10500 our alt and cabin alt were the same. At 9500 our cabin alt was below 10000 and the CAS warning was settled. We were above 10000' cabin alt for maybe a minute but I suspect it was closer to 30 sec or less. ATC asked If I would like to [request priory handling] and I declined. I should have said yes. I did ask for deviation to ZZZ2 and Runway XX.