G'day Sue,
As far as bread & butter $ events are concerned The Big Mile usually runs flat out down the grassed side outside fence through the final 16th of the race & if his charge salutes the judge he will proceed to abandon all aspects of self control, leap up and over the rail, rush out onto the track and proceed to kiss and bear-hug the driver. In big $$$ events the reaction is even more pronounced.
Fines wise, if your horse wins & your driver gets jammed up for slow sectionals or out of position at the start or whatever then I think it's good form to pony up the cash on their behalf. I would. Even if they get beaten I'd consider it. Finishing last might not fall under that banner though. When they're out there doing their absolute best to win the race for you then it's the right thing to do to cover them, IMO, unless of course it's a case of reckless or foul driving or whatever but I've never encountered that yet.
Interestingly, most of the TB owners will leave the Hoops swinging in the wind if they get fines for too many whip shots or whatever, not exactly sure what they get fined for to be honest, but a couple of mates of mine are Jockeys and the TB owners are quite often miserable bastards in that regard.