The CG assets were (for about the last 10 years) supposed to be tasked through the ARCCK but could self task within 30 nm of their CG MRCC and then advise the ARCCK.
The same happens with many mil units, the local CG give you a heads-up and then phone the ARCCK to get them to officially task you.
As Leopold says, there are so few military SAR jobs nowadays, it makes no sense to have separate tasking authorities.