I don't suppose you could share the full screenshot, or screenshots of a couple different points in time? Arrows of that color are from either right click commands or 'search and destroy' in my experience (is there another way that color gets assigned? I'm away from the game right now.) They almost always point towards the objective that the AI is assigned to, even if its having trouble/refusing to actually follow the order. That tells me that either this unit has been assigned to an objective in the bottom of the screen we can't see, or that its on 'search and destroy' mode.
If its on 'search and destroy' mode, then its going to ignore all regular commands - I've noticed some funny behavior in that mode as well where they don't always go towards the main bulk of the enemy, and I sometimes wonder if in that mode there is some sort of issue where they only consider their own sight radius instead of all the map exposed by allies as well, or if there is some sort of 'exploration' imperative? The sight radius thing might explain this screenshot, as I don't think any enemy are in range of its own sight. I honestly don't use the mode very much but I wonder if there is a bug with it.
[Edit]
Re: officer personalities, I think three are relevant. 'Aggressive' is the standard type of officer for good AI performance on ships that you want to fly towards and attack the enemy, but still be reasonably careful. Full Assault on top of aggressive produces good results imo as then they will start freely spending missiles.
'Reckless' is a specialty tool for ship that you want to, well, recklessly attack the enemy. SO ships, big armored bowling ball distractions, etc. Just be aware that because the ships will charge in, if there isn't enough aggressive/reckless support to help them they'll just die, so if going for one reckless its often best to have some more so they all attack together. Or just have an Onslaught be Reckless and let the aggressive rest of the fleet take advantage of the opportunities it creates (with orders from the player to help guide them in.
'Steady' is also relevant for ships that need to be careful and stay away from situations where they are outmatched. Carriers, overfiring missile ships, fragile but fast frigates that are disctractors, dedicated kiting ships (artillery sunders, ion wolves, hvd vigilances maybe even gauss conquests though aggressive is fine on them).
Neither cautious or timid are useful, though at least a found cautious officer can be retrained into steady.