Ok after more testing with transports, you definitely can't load troops on a transport just by clicking them on the world map. The only way currently to load troops on a transport is by putting them in a town and than doing it. If you transport your troops to another island for example, your troops are now stuck there unless you build a town or attack another town and are able to than load them on the transport.
Also, clicking the tab for details on a transport crashes the game.