2 cars I've had problems with have been the Alpines, and the Triumph Spitfire (both heavily upgraded). I have not been able to properly tune them for Trial Mountain online. Nothing seems to help a great deal.
The problem seems to be much less on other tracks, some barely a problem. Trial Mountain is blatantly obvious... though I'm not sure why.
Otherwise, I usually don't see much difference, if any, online with cars I've tuned in Practice mode. (Practice mode with tire wear on, track grip real, and all aids off.)
But I'm good with modulating the throttle. I really think the more you are heavy on the throttle, the bigger the difference you will notice online.
I think the differences are because of latency... so the more fussy a car is, the more minute corrections it requires while driving it, the more difference there will be online... because your tiny adjustments while driving may be offset from the feedback you're getting (on the screen for example). If you're heavy on your inputs, the worse the problem will be. The more fussy the car, the worse the problem will be.
It may only be offset by milliseconds, but the human brain is able to process information differences of milliseconds. This has been proven scientifically, but it should be obvious to anyone who knows anything about racing!
In racing, .001 second is tracked... So obviously it counts.
If your input is even .001 off from what you're seeing, something's going to seem off when you're driving. But it might not be obvious to you exactly what's going wrong. (I couldn't say the numbers, but it could be that if it's even offset much less than that, maybe you could sense it. I don't know.)
This is not something you can dial out completely with tuning, as such. At least I can't think of a way it would work.
It may FEEL like a tuning issue. And tuning can help. But it can't solve the problem. And there's no one tuning option that's going to help for every car. It's completely dependent on the various issues with each different car, what could help.
Append: Minimizing latency sure could help also.
I've posted my suggestions before, such as here today:
https://www.gtplanet.net/forum/showthread.php?p=5331366#post5331366