USB KVM switchers are a bit of a mixed bunch.
Some of them are quite clever and act as a real 'host' to the USB keyboard & mouse, and present themselves to the host PC as real mice/keyboards even when switched the 'other way'.
Some of them are just 'dumb switches', and simply contain a series of (hopefully) USB-spec switches to re-route the data to/from the relevant unit. (Think video crash-box)
I'm not entirely sure which variety is better.
The 'smart' KVM will switch faster, but runs the risk of misidentifying itself or the connected devices, while the 'dumb' KVM requires the host to re-identify the connected devices, and if it doesn't turn the connected devices off for long enough they may not attempt to re-connect.
USB 2.0 adds an additional layer of complexity to this, as at the first attempt to connect it will try to use the full-speed USB 2.0, then again in High-Speed mode, and finally in USB 1.1 mode.
As to the question of PS/2 - the ports do physically exist on a Congo Senior, but you can't access them as the CPU metalwork hides them.
PS/2 KVMs are generally better as PS/2 isn't officially hot-pluggable, so all decent PS/2 KVMs host the keyboard & mouse themselves and pretend to be a single unit to the host.
Unfortunately there does appear to be something strange with the KVM unit itself, so you'll need to contact that manufacturer.
As a temporary workaround, you could simply use separate keyboards and mouses for the two consoles, only sharing the monitors themselves.
If you can live with the slower USB pen drive access, it is possible to slow a Congo Senior down to USB 1.1 - however they've not been extensively tested in that configuration.
Keep on trying till you run out of cake.