Really, I have had DI water in systems for years and no growth unless it gets contaminated by something. Bacteria can't grow if there are nutrients available.
But it is easy to get a system contaminated and then it's all over with. Like I said earlier, we use Optishield Plus on all of our water cooled lasers. It should work with whatever you have.
https://www.optishield.net
You could just parallel the cooling loops with a couple check valves and set the temps the same since the Rofin just uses a single loop through the head and to the power supply. I dont know what it's going to take to control that chiller, it looks like it has a control panel on the front so hopefully you can set it up from there. Without hard specs on the chiller and the capacity of each individual loop its hard to say. You could run the head and power supply off separate loops but I dont think there would be any advantage. if you did you should put a water flow switch in series with the power supply and tied to the PSU enable to protect that since there is only a flow switch in the head.