This happens to me as well, and to all Inquisitor's who don't use the race-default voice as far as I've heard from other players. Changing it back and forth in the Black Emporium has no effect.
I am on the Xbox One, and have a female human Inquisitor with the non-default race voice (american), which plays during conversations, but the default (british) plays during *efforts* lines (jumping, attacking, yelling) as well as lines while on mounts. It's fairly immersion-breaking to have your character's voice and accent change every time you initiate combat or use a mount.
To be clear, if I used the british voice on a human or elf, the voice would be consistent, or if I used the american voice with a dwarf or qunari, it would be consistent. It's when you use the american voice with humans and elves or british voice with dwarves and qunari that the problem arises. As far as I know this applies to both genders as well. So it seems like this is simply a programming oversight and all that needs to be done is to correctly make your voice correspond to the one you chose, not the race-default.
It's not the end of the world, but I hoped after 9 months and 9 patches this could be fixed. Hoping is still can be! Thanks.