Hello!
(quick note: community manager already replied to this post, I don't know if any of my suggestions are correct at all, I'm giving it a shot)
The problem might be that your employees are already assigned to one room, and don't realize "go to this room" = "perform surgery task". The AI might also just be a bit off here (it does that sometimes). There's obviously problems with AI, so perhaps there isn't an automatic response, even though human intelligence would consider this extremely simple.
Also, if you bought a pre-built clinic, and messed with the surgery room too much, it might not be seen as a surgery room to the staff Sims, regardless of the fact that it meets the requirements. (Haven't tested this, just a theory.)
Might just need to try and re-arrange things until something works.
OR
There is also the likely solution that your staff doesn't NEED to perform surgery. I could get through days without even needing to look at the surgery room, and my staff just did all the procedures in the regular room, then billed the customer. If by "leaving it to you" you mean that they just abandon the room, they might be slacking off or something. Or maybe the rooms are just broke (as mentioned earlier) and the AI makes its best guess as to what to do. It may just be that you have to perform the surgery.