Oh, I see. So maybe that's why the times messed up. Time on MP is controlled server-side. When you switch servers or to SP, the game can't tell what the real time of your trip is.
If I may suggest, you should save up some money and buy your own truck before hopping onto multiplayer. Or get a loan. Once you have your own truck (and is fully rested) you should be able to do Quick Jobs in MP just fine. That way you can make some cash faster than you'd do driving your own truck for that way you won't have to spend money on fuel and repairs. The loan should be paid in no time. I also recommend that despite doing that, you use your own truck for the longest trips. You'll be spending money on fuel and repairs but you'll also be getting a bigger paycheck (supposing you don't crash/damage the trailer and don't get late). Go with Quick Jobs for shorter trips.
P.S: If you want a good truck for the best price, I recommend buying the Volvo FH16 Classic. Not because it's what everybody uses, but it's because it's the truck that offers the best specs for the lowest price. About 99k (or 98k if you remove some stock accessories) and you can get a simple model with a engine of around 580HP (or was it 560? I forgot the exact horsepower), which is upgradable up to 750HP (the best in the game). Other truck brands only have weaker engines for that 99k price tag. And they cannot be upgraded past 700HP. (Except for the Scanias. They can go up to 730. Though Scanias are more expensive than than Volvos.)