I use the MoXF together with a Roland BK-7m. This should be very similar to using it with a Tyros. You can also use the MoXF in performance mode, it also sends your keyboard activity on midi channel 1 even if you have allocated different parts to different key zones. That way you can use different MoXF sounds for upper / lower.
In the Tyros you might have to check the receive channel for styles, it has to be set to channel 1, too. (At least in my BK-7m there is a setting for style midi receive, and if the channel doesn't correspond, there is no chord recognition even though you can play sounds of the external instrument).
Using MoXF sliders for the Tyros parts is probably more complicated, you would have to program the MoXF sliders like sliders of a master keyboard. I haven't tried that with my BK-7m.