Trump didn't totally shut down travel w/China. 40k people came in after that from China and that wasn't because of Democrats. Some were citizens, some were green card holders or had moved away apparently and wanted to come back, etc. I remember seeing a post by an American in Italy who said they were going to self-quarantine over there and not come back in case they were a carrier, which I think was a good idea.
But no, he didn't do any of it to keep people from panicking in the sense that he was trying to help us, the panicking he was worried about was people selling off their stocks like those 4 senators or changing their views about him as a president. Because he knows the state of the economy reflects on him, he'll lie, cheat, steal to keep the numbers up, even if they're inflated and fake. The "liberal media" wasn't trying to incite anything the way Trump is trying to incite civil unrest right now. It's ridiculous what he's doing with his base.