They're only +15 and factory rims were +38. So it was coming into contact with the calipers without the spacers, which are 1.5" (38mm.) They are 'far out'...by the +15, and then by those tires are wider by another +16 on each side (than stock 285s), if I understand the math. Seems like more than +31 sticking out there though. Math is hard.
So if the wheels you have are a +15 offset, and you added a 38mm spacer, you turned them into a -23 offset which is why they are sticking out so much. Offset is measured like this:
The more positive offset a wheel has, the farther into the wheel the axle hub is. The more negative the offset, the less the axle hub sticks into the wheel. You gave yourself negative offset so the axle hub isn't in as far as it should be for proper fitment and suspension/steering geometry. If your wheels were already +15, then that is 23mm too little offset from where they should be, depending on the width . If these 18" wheels with only a +15 offset were hitting the rotors, even if the rim is a 12" or so wide rim, they should easily clear the calipers. The factory aluminum wheels are 16" x 7.5" and clear the calipers just fine. Looking more closely at your pictures, I have a feeling the wheels are hitting the face of the calipers with the spokes, rather than the inner circumference of the wheel as one usually sees. This would explain needing a spacer to move the wheels out far enough so that the spokes aren't hitting the calipers.
Truthfully, you need to return those wheels and get some that fit correctly. There is no valid reason 18" wheels should not fit correctly aside from the issues of improper offset and insufficient clearance between the spokes and the calipers. If you bought those from a wheel shop (either online or locally) then they did you a huge disservice by selling you wheels that did not properly fit for the application.