I've had the keyboard prompt come up 3 times, which is a success rate of maybe 5% considering the number of times I've entered text on ATV after installing the new tvOS.
The few rimes it was triggered correctly, it came up on all my iOS devices (2 iPhones 2 iPads) in a split second. It's always either all of them or none. So the fault would have to lie with the ATV, hence logging in and out of iCloud on the iOS devices is likely a dead end.
Pretty much everything having to do with tvOS 10 and wireless communication is glitchy. I can no longer wake the ATV up via the Remote app(s), I have to wake them by starting an AirPlay session. Also can't register more than one iOS device as ATV remote. The first is unpaired the instant I pair another.