Hey! I think I have the answer for you.
Regarding time that passes during a job:
On TruckersMP the time always passes because it's synced with other players. If you have started a job on multiplayer and leave the game for long time, it would be better to complete it on singleplayer. If you start a job on singleplayer, complete it on singleplayer because in multiplayer the time passes non-stop, and the time may pass while connecting to the server.
Regarding the drivers:
The drivers doesn't work well on TruckersMP. In order to have income from them on multiplayer, you have to teleport to garage or service, or go to the rest area. On singleplayer they work properly.