Alright cheers. 
So the official ruling will be; supports, skills, and other things will not affect staves. Staves are a separate thing from combat, so things that affect combat (terrain, skills, counterattack, supports, etc) will not affect staves. Staves are all about raw stats.  
EDIT: 
In an effort to keep aliment staffs relevant, they will not lose quality for misses (which I'm not sure if by RAW they do or not) but will give no EXP on a miss.  
Klaren since Hoshiko killed the rider, you have your turn refreshed. If you just want to move to the same spot instead that's fine.