Transferring Int'l to Int'l at JFK

In September, on our way back from Tahiti, we are due to change planes at JFK.
We fly into T4 on Air Tahiti Nui and out again on VS from the same terminal.
I understand that we will have to clear immigration, do we then have to go through customs, back to the main VS check in and check in as normal for our onward VS flights, or will we get our boarding cards at Tahiti, and just go and drop our bags back off at a transfer desk somewhere?
We're only on the ground for around 3 hours I think so it could be tight if immigration is busy. I guess that as we are through ticketed, that shouldn't be too much of a worry though as there are 2 later VS flights.
Thanks for any help.
Mark
We fly into T4 on Air Tahiti Nui and out again on VS from the same terminal.
I understand that we will have to clear immigration, do we then have to go through customs, back to the main VS check in and check in as normal for our onward VS flights, or will we get our boarding cards at Tahiti, and just go and drop our bags back off at a transfer desk somewhere?
We're only on the ground for around 3 hours I think so it could be tight if immigration is busy. I guess that as we are through ticketed, that shouldn't be too much of a worry though as there are 2 later VS flights.
Thanks for any help.
Mark