If I recall correctly, there's a damage limit in the vanilla game, after which followers will revert to their default bow. I want to say the base damage of both bow and arrow have to be between like 15 and 22. Don't quote me on the numbers, but in practice, I was able to give them Dwarven bows with steel arrows, but when I hit Elven bow I had to strip them of arrows and they'd use their default irons ok. As soon as they get shot with a higher level arrow, though, they begin using them. If that exceeds that limit, they'll stop using their good bow and shoot their new arrows out of their default bow instead. I got into the habit of checking them for contraband arrows after each combat.
I'm not sure if this has been fixed by the unofficial patches or not. It was an issue for me on console and during vanilla PC play. Now that I use AFT, they use what they're told to use.