Top Drives Multiplayer Events are A-Synchronus, meaning that when racing against opponents you are racing against their Ghosts, which is a recording of them doing the race, showing the cars they used and in which order.
When you are offline, other people may come up against your Ghost, which is your last match that you played. So ensure that your last match is with your best cars!
These races also affect your score, so you can gain and lose points while offline in the same way as if you were racing online. This can be especially exciting when approaching the end of an Event where lots of players are scrambling to play as many races as possible with their best hands to get the best prize... while those offline are hoping that none overtake them with the hand they last played!