New front tires

I need a pair of new front tires for my Kubota L2800 4wd tractor. the tires on it were 30 X 9 X 15. after some discussion with my tire guy, we think that these were not the correct size. According to tractor data, the tires should be 27 X 8.5 X 15. He said if we put the size that was on there back on, it could damage the transfer case, because the ratio would be wrong. We have ordered the correct size, but my question is has damaged occurred to the drive train due to improper size tires?
BTW, I bought this tractor in July, and it is a 2006. I have no idea how long these tires have been on. They are more of a truck tire type, and the new ones I have ordered are more like the rear tires, but obviously smaller.

Thanks

Unfortunately, I don't have the owners manual. Using tractordata.com to get the info on the tires.

Thanks for the link, I will download the manual. So, I have the industrial rear tires (15-19.5) but someone put 30-9.5-15 tires on the front. They are obviously larger then what was recommended. I'll put the right size back on. I guess they, and now me, was just lucky that no problems showed up with the front drive.
Art