There is no problem purchasing one way tickets and then purchasing the return tickets.
It is done quite regularly & I've done it myself almost every time I've purchased tickets...as more often than not it works out cheaper for me to purchase this way.
If I'm reading your information correctly...you plan on purchasing your return tickets just before you arrive here in Jamaica...that's all you need...proof that you're returning back home with a return ticket in your hand before you arrive here.