CDJ/Slink-e Power up CD Players?

I'm using a Slink-e & CDJ to control a Sony CDP-CX450 & Sony CDP-CX57, which are connected to the Slink-e on one Slink bus. Last night I tried turning off the CD players while CDJ was running. It was strange! Depending if I used the Sony receiver remote power off (which powers off all Sony devices), the CX450 remote, the CX57 remote, or the power buttons on the players, I got different results. Some devices would be off & others on. But the most common scenario was the CD players would turn off ... then turn on again all by themselves!

I closed CDJ & sanity returned ... a power off meant a power off!

Presumably CDJ is turning the players off. Is there any way to power them off overnight, while leaving CDJ running (which I prefer, especially because CDJ startup is SLOW)?