Explain this:
 

I'm adding borders on a quilt top. When I measured for the first border my numbers for the length were: Top: 89.25 Middle: 89 and Bottom: 89.25. I cut the borders at 89 and sewed them on. Then I measured the quilt for the second border and my measurements became: Top: 93.5 Middle: 94.5 Bottom: 93.5.
How did middle measurement become an inch larger than the others? The strips were all cut at the same width and I used the same seam allowance.
What should I cut these borders at? Use the middle measurement? Average?

use average and ease in the borders.

Agree 100 %

To help ease in the borders, should they go on the bottom (next to the feed dogs)?

First, measure again to be sure you got it right. It's easy to make a mistake when you are measuring anything larger than a yard or so. Also be sure you're not stretching the quilt while you measure and that it's pressed evenly. It's not terribly unusual to have an inch difference, since just 1/16 of an inch difference in each seam, spread over 16 seams, equals an inch.

Usually the part that is longer and needs to be eased in is put next to the feed dogs.

If you ease the borders you'll likely get wavy borders.

Yes, you want the bulkier fabric next to the feed dogs to help with the ease. Another trick I saw on a sewing program long ago was to hold your finger behind the presser foot and let a bit of the seam length bunch up tightly behind the presser foot. With a seam that long, let go and repeat as often as necessary. That and the feed dogs should help ease the excess. But I also agree - re-measure. It sounds awfully odd that your dimensions would be off that much after adding a single border.

It sounds like you did everything right. You measured the quilt top, averaged the measurement for the borders and eased in the top to the border fabric. I have no idea why the middle suddenly is wider than the top and bottom. Good luck!

That happens to me all the time! I'm glad to know I'm not the only one.

Which border did yo sew first? If you did the top and bottom first and then the sides this would make sense to me. I always have odd measurments because I often go off on my own and do my own thing so it is not the pattern size it should be.