The CT-1870 is not a hard disk controller... it only works on non-bootable drives like optical. Unfortunately, it was never supported in Window 95, only in DOS mode.
This might or might not work... in Control Panel double-click Add New Hardware, select "no, I want to select the hardware" , click next, then select cd-rom controllers, select Mitsumi then in right window select the first listing, "Mitsumi with double speed controlle"r. Now reboot and if you have the drive connected, check in My Computer to see if you now have a drive listed. If not then go into the cd-rom controller properties and play around with the i/o address... most are either set to 260 or 270, and keep rebooting after each change to see if the drive will appear in My Computer. If this doesn't work, I have no other fix.
On second thought, the CT-1870 may be an IDE controller... I believe it's the CT-1810 which is the proprietary controller. It looks like ide, eg: has 40 pins but is not ide. Does Windows 95 not detect it automatically when you install it and power up?