I wasnt able to reproduce this.  Maybe something else is causing the delay.  If you can link your save game I can test it out.

Ok, I have started a new game and my sovereign just got Rain of Arrows but the problem is not repeating itself.  So, it must not be directly linked to Rain of Arrows.  I have the old save with my sovereign near some enemy units so you can try it out.  I just loaded it and the delay happens again as soon as I attack and auto-resolve a combat with my sovereign's army.

How can I link the save for you to test out?

I also see this issue, but I never use auto-resolve - it just happens randomly when I tell my hero to use the Rain of Arrows ability.

I would say it happens more often than not, but definitely not every time I use the ability. I have not noticed similar effects with other abilities (I have about 30 hours of playtime).

I don't have facts to back this claim up, but It seems to me like the bug is less likely to happen the first time I use the ability in a session, and more likely to happen if the game has been running for a while.

I'm running whatever the default version of the game available on steam is.

dropbox.com or another file hosting site.

I've got dropbox actually.

Ok...let me try and link this.  In this save, my sovereign is in an army and there is an enemy nearby you can chase down in a turn to check on the delay.  Just auto-resolve the battle and you will see a delay.

https://www.dropbox.com/s/2ye8h1zjwppxl28/Ben11a.EleSav