Considering the just announced new MacBook isn't yet generally available there are very few people, if any, that can say they've actually connected a LaCie USB-C (USB 3.0) external drive to the just announced new MacBook and booted either OS X or Windows from the external drive. That said, I'd be very shocked if one was not able to boot any OS that supports booting from an external USB device while connected to the just announced new MacBook that isn't yet generally available. Especially considering the just announced new MacBook only has only the USB-C port (and an audio jack) for any type of physical expansion capacity it would be insane that past normal functionality was not capable.
You should not of had to install the drivers manually. If you right click on setup.exe from the "Boot Camp Support Software", you should be able to select compatibility mode. You say you formatted the drive. It would help if you explained what utility you used to do this. My concern is for how Windows determines the drive partitioning. For your model/year Mac, Windows should be installed in MBR/BIOS mode.
If the "Boot Camp Support Software" is installed correctly, then you can select the startup disk from the Boot Camp pane on the Control Panel.
Another option which works on most later Macs, is to hold down the alt/option key on startup. When the icon labeled Windows appears, hold down the control key and select Windows. This will make Windows the default operation system.
Here Is Some Advice on the Boot Camp Support Software.
According to the Apple web site "Install Windows 7 and earlier on your Mac using Boot Camp", the proper "Boot Camp Support Software" (BCSS) for installing 64 bit Windows 7 on your model Mac is "Boot Camp Support Software 5.1.5621". According to the Apple web site "Use Windows 8.1 on your Mac with Boot Camp", your model also supports 64 bit Windows 8.1. For this version of Windows, Apple requires you to use the Boot Camp Assistant to download the BCSS to a flash drive. You can download this software without installing Windows 8.1 to your Mac.
One of the machines, I have access to, is a 2011 iMac. It uses the same version of BCSS as your Mac mini for the installation of 64 bit Windows 7. I verified that the BCSS for installing 64 bit Windows 8.1 on this iMac is exactly the same as for installing 64 bit Windows 7. I have no way of verifying if is this is also true for your Mac mini.
I thought I used the procedure given in the comments below to run the BCSS on the 2011 iMac with 64 bit Windows 10 installed. Now that I think about it, I may not of had to.
Eventually, the BCSS is released in sets of versions. As far as I can tell, only version sets 4, 5 and 6 can be downloaded from an Apple web site and/or through the Boot Camp Assistant. Older sets exist on the Snow Leopard (OS X 10.6) or older DVDs. Some (if not all) of the version 4 BCSS downloads contain a Bootcamp64.msi file. I know this to be true for 4.0.4033 and 4.0.4255. Most (if not all) of the version 5 BCSS downloads do not contain a Bootcamp64.msi file. I know this to be true for 5.1.5621 and 5.1.5640. The version 6 set is irrelevant, since Apple does not officially support Windows 10 on 2011 Macs.
This leads me to the conclusion that you are using the wrong BCSS.
You should probably install El Capitan (OS X 10.11) and download the BCSS using the Boot Camp Assistant. Or at least, you should be download "Boot Camp Support Software 5.1.5621".
Best Answer
This procedure will not work for your 2015 Mac. Step 6.2.5 states: "Run: clean". The next step (6.2.6) states: "Run: create partition primary". This indicates the external drive is using the Master Boot Record (MBR) partition scheme. The 2015 and later Macs can no longer boot operating systems using this scheme. The question you refer to involved a 2014 Mac.
This procedure you reference requires you to download the "Windows 7 Automated Installation Kit" in step 3. Later, step 6.2.4 uses the
imagexcommand from this kit. This command has been deprecated and should not be used with Windows 10. The replacement command isdism.exe, which is included in the Windows 10 installation iso. So steps 3 and 5.3 are unnecessary.This procedure may be adapted for your model Mac. One change would be that the external drive needs to be using the GUID Partition Table (GPT) scheme. This is probably not the only change needed. The accepted answer to the question "Unable to boot Windows 10 from Bootcamp external HDD" documents another possible change that may be needed.