You have it backwards - if you're paying in USD, that would be rounding DOWN. If you owe somebody $100JA, you owe them $1.15US. If you owe somebody $500JA and give him a $5US bill, you have short-changed him $.75US, not given him a tip.
Seems odd to me, but I see this happen all the time, and the Jamaicans may be unhappy but accept it.
I don't find it difficult at all to stop at the bank or a cambio, change money - INCLUDING asking for small bills - and then just pay in Jamaican.