Budget's site says per day.
Lifemiles' site sayd per rental.
My guess is this is a typo on Budget's site...but it is a typo they should honor...that said, YMMV. If you want to risk it, I'd say give them your lifemiles number, wait for your 500 miles to post, then lobby budget for the 14.5K additional miles they owe you. Of course, this is going to cost you $22.50...
I discovered this same thing back in October, so used my lifemiles number on a 2 day rental; I was only given 500 lifemiles, not 1K.