Initially thought this was a beacon bug, but may be associated with the speed boost itself.
I play split-screen multiplayer with a friend.
We have all beacon effects up and running in survival mode.
Every effect OTHER than speed 2 works with both players.
The speed effect works on player one (me) but NOT on player 2.
This seems to be the case whether we use a beacon or a splash potion.
However, if player one enters the end or the nether, player 2 immediately gets the speed 2 effects. When I return to the overworld, the effects disappear.
On the status screen for player 2, the speed 2 effects appear to be there: ie there is a timer counting down from 0:08. It just doesn't work.
We are both logged in to xbox live.
We have not tried it on separate Xbox one consoles.