I ran into this too. I found the most effective way to get the BO to take part in the battle was to tell them to attack something directly. This would often prompt him to run up and start to smack things.
The other way is to put yourself closer to the enemy. By default they follow you and if you get into close proximity it will often trigger him to attack.
I get my melee tactical officer to beat up on guys by choosing a target and then clicking for my melee officer to do a Leg Sweep. He generally continues beating on them, but even if he runs back he knows to start whaling on anybody who comes near.
Unfortunately, I don't like how my melee officer attacks - it's too slow. If I start punching a bad guy myself I can toss a continuous stream of punches provided that I'm not stunned or held or anything like that. But my melee officer will throw a punch, crouch, wait, throw another punch, crouch, wait, throw another punch - etc. Cryptic really needs to improve this.
I'm hoping to myself that if I hand my melee officer a Bat'Leth, which can be bought at DS9 and be used at the rank of Commander, he'll strike more swiftly.