Personally I think it's inevitable the next consoles will use it, DXR was a cross industry effort, AMD's architecture(Presumably spanning the PS5, Xbone, Ryzen & Radeon) probably won't be as dedicated to it as NVidia's or commit as high a %age of die space to RTRT, but their cards are already potent enough at RT (With a fairly mature non-realtime pipeline) that AMD doesn't really need to take the same degree of change in direction to offer the support, especially with a 7nm launch.
As well as this, I can't see there being anyway that the game industry is going to diverge in directions so sharply with the next console generations, with investments in completely different rendering engines for different platforms. We know for a fact Microsoft has thrown a lot of money at getting RTRT out, so an Xbone release at the very least would seem all but a given on at least one model, and given how wide the support is for DXR amongst cross-platform engine developers and the like, I feel that confirms it, the support for DXR amongst such a wide variety of companies wouldn't exist now if it was expected to be a single-manufacturer product for all of 2019.
DXR's support at this stage arguably seems stronger than DX12's was, but certainly seems much more in line with past Microsoft-led industry standard API's as we'd expect for a wide-ranging feature. Compare the support for this to GPU-vendor-specific technologies(What some expected DXR to be due to NVidia's early deployment of their accelerator units, and the only thing that would really stop it from reaching consoles) and the difference is night and day.
