From what I have heard, yes, you need to have runemate open in the background. I also make sure that I open the RS client via runemate, just to be sure - but I am not sure if it makes a difference.
Regarding how it actually works, I am not certain. I did message Arbiter but I suppose he has been busy. I also would assume that giving out the exact mechanics behind it is not going to be too profitable for the developers.
One thing I have noticed is that the bots tend to misclick, the same amount as I would missclick. I am not sure if that is the bot authors built in antiban or a combination of both, but I feel the scripts run to my playstyle. I even thought the amount of misclicks was some kind of bug, until I realised how much I misclick after smoking a joint, haha.
I could be totally wrong, but my advice to you would be to see how differently the same bots run over time, after you have put in more hours of legit play in the client. However, we never know, it could just be a marketing ploy.