Tina took the suitcase to MACUSA where Newt and Jacob emerged, but were they trapped inside until then? A magical suitcase from which you could not extricate yourself when locked from the outside seems very dangerous.
Possibly, possibly not. The screenplay indicates that Tina was under the impression that she'd trapped them.
NEWT (O.S.): (to JACOB) In you hop.
[We see the case sitting alone below the bridge.]
[TINA quickly appears around the corner and hurriedly sits on the case. She closes the catches, looking shocked but determined.]
That being said, it's not entirely clear whether Newt and Jacob had even noticed that they were locked in until Tina bashed on the lid. Additionally, the locks on the outside were simple catch-locks and the case had apparently not been made "muggle safe". I think we can reasonably assume that pushing up on the lid from the underside (which is essentially a trapdoor) would have broken the locks in very short order.
As far as the overall security of the case, Newt's niffler was able to escape in an earlier scene by simply levering the case open. Assuming that Newt didn't want to apparate out of the case, it's possible that he could have used his wand to undo the locks from the inside (Alohamora!) or just reached out and undone them from the outside by hand.
The locks also seem to have a tendency to open when the lid is prodded from the inside.