I have always thought that in order to conduct naval transport that units had to start the action round in a port. However rereading the rules they don't specify so. So can land units move into a port and then conduct naval transport in the same action round?
Since it makes a pretty big difference for many of the rules:
I assume you mean impulse where you say round. Impulse is just one Card-Play when it is your turn to do so by Impulse Order. The round is the full collection of diplomacy phase, all impulses and the winter parts. There are at most 9 Rounds in the game, however they consist of many impulses.
That said: The formation has to begin the "Naval Transport" ACTION in a port. However within the same impulse they may already have taken "Move Formation" actions to get to that port.
One impulse often consists of more than one action.
So yes, you are free to move a formation into a port and conduct a naval transport from there within the same impulse.