Yes there are general rules for regular TOUR caddies, but not for local caddies.
The agreement, before the tournament started was:
$1k if Kuchar missed the cut
$2k if Kuchar made the cut
$3k if Kuchar made Top 20
$4k if Kuchar made Top 10
Kuchar gave him an extra $1k above what was agreed upon.
So, no this is nothing different.
I agree there are unwritten rules on what caddies get, but those are for the professional caddies. Not a random local guy who regularly makes $200 a day.