There was no confirmation of a negative test to get on the plane. It was STATED that the arriving destination required it but it was no confirmed before travel. The qRT-PCR is not an acceptable test (right now) so you will be subject to re-testing and quarantine until the results are back.
I guess this is not an issue but I would definitely try to avoid testing in SXM just in case of a asymptomatic positive (or false positive) test which could create a fuster cluck of events
..and how did you complete the online entry form with an inappropriate test?