I believe I know the exact and logical explanation.
I is a pretty simple one, actually. I kind of feel stupid not to come up with earlier:
The following picture is from the Intel Datasheet for the ICH9 chipset regarding USB functionality. I know your board uses a different chipset, but the general functionality is exactly the same:
What you see here, is the switching logic for a total of 12 USB ports. Behind the ports are actually eight (!) controller interfaces: 6 for UHCI functionality (each controls 6 ports) and 2 EHC interfaces (USB 2.0), each controlling 6 ports.
Depending on the USB device that is plugged in, the ports will be literally switched to the correspondong controller. Now, that is not hard to understand and pretty obvious, when you look at the picture.
Now, in your case a third USB controller Interface (XHCI) comes into play the ASMedia 1042, which does only particular thing:
It is implemented to support USB 3.0 (XHCI) but not in terms of being a seperate controller, but is actually integrated as an extension to the already present Intel UHCI and EHCI interfaces. In other words: It will give two if the USB ports the possibility to not only switch between UHCI and EHCI but will provide them with a third switching option
: XHCI (which is the ASMedia 1042 XHC Interface).
Because, when it comes to USB devices and ports, the assignment to UHCI, EHCI or XHCI is only realized via such a switching logic, the system will literally switch the two ports in question here to either Intel UHCI or Intel EHCI when a) no USB 3.0 device is present or b) the ASMedia controller is disabled in UEFI/BIOS Setup.
As the connection between USB Ports and corresponding controller is NEVER a one way hardwired matter, but one that is based on switches, one and the same USB port can be physically assigned to either the Intel or the ASMedia controller, depending on the connected device.
Now, as you can see, this explanation actually explains ALL the symptoms you mentioned.
According to the Intel Information regarding the chipset used on your board:http://ark.intel.com/products/52806/Intel-BD82H61-PCH
... the chipset actually provided support for precisely 10 USB ports, which means that from the Intel side, there will be 5 UCH interfaces able to control 2 ports each and another two EHC Interfaces designed to control 5 ports each.
However, the board has only 10 USB Ports altogether, not 10+2 as one could expect (10xIntel + 2xASMedia). So the only logical explanation here, is that, and I already said that, two of these ports have a third switching option for XHCI (ASMedia) operation.
Now that we have explained ALL the things you keep pointing out as normal and logical system behaviour, all you need to do is plug in an USB 3.0 device. The port will then automatically be switched not to Intel UHCI nor to Intel EHCI but correctly and logically to ASMedia XHCI.