A fresh Mint install, using the whole disk, should not show any reference to booting Windows.... no matter if it is a new computer (UEFI based) or older computer (MBR based). Both scenarios would erase the Windows bootloader completely.
Also, the "Windows boot manager" is not a screen that shows up during boot. Are you seeing the GRUB boot menu? Can you show us a picture? Have you tried to boot on the Windows you're seeing?
You might just try to reinstall Mint again, being sure that you are choosing "use entire disk."
Mr. Mushroom. You didn't actually say how you partitioned the hard drive nor have you said how many hard drives you have. If, like Atanere stated, do a new install and tell Linux to use the entire disk (and don't have a second disk) then it will completely wipe out anything WIndows related and you won't see it in Grub. Actually you won't see Grub itself without hitting esc during boot because it just automatically picks the only OS. However, if you leave the Windows partition or disk there without removing or reformatting it, then when you install Linux, Linux will still see something there and list it in Grub.
Also like Atanere said, the Windows boot manager isn't visible anymore. Back in the old days they had a boot menu like Grub but they removed that a long time ago. It was in Windows NT 3.51 and maybe 4.0. When they went to XP, they removed it, if not earlier.