I have been doing the challenges both as a regular member and premium member, and haven't seen any difference, so don't think premium members are being given any advantage. I have played 136 games, with 16 firsts, 21 seconds, and 22 thirds, and I do not do any cheating. I am by nature a very analytical person, and have seen patterns in the cards that have helped me over time get faster. Some of my observations are:
I am not positive this is right, but it appears to me that the clock does not start until you click on the first card, so I can look at the cards in games like FreeCell or Pyramid and get a strategy before I start. Even in TriPeaks planning ahead can help.
Going back can be smart, even if it takes a little extra time. Like in TriPeaks, you may try one combination and think it worked well. But you may find if you take fewer cards on the first play, the second play has allowed you to take a lot more cards off the board. Or you are getting toward the end and you could pick one of two cards at the end of a string. If both will expose another card, I will often try both. Just remember if you are doing a game to beat a score, you need to go back to the start of the run to get the full score.
In Pyramid, I almost never play two cards from the deck to make a match. I leave them for use later. Sometimes I find that after playing a card from the deck to make a match on the pyramid, doing a match from the deck helps open up a card that was not available to be before. For example, I play a 5 on an 8, and it exposes a 7. Although no six is available, the two cards showing are a match and there was a 6 one card back, so I play the match on the deck and use the 6 to play on the 7. Usually I only do that late in the game. And before I start any Pyramid I look for the two cards in the second row from the top. I know those cards will need a match, so I try to preserve the matches and avoid playing a match earlier from the deck if a match is available later from the cards on the pyramid.
That being said, there has to be cheating or AI going on. My time for tonight's game is 49:06 which puts me in second place thus far. The first place time is someone who has 3-4 times as many high scores as I do and has a time of 33:39. That player had done twice as many events as I have, and perhaps by the time I have done twice as many as now, I will be faster. So I don't think he/she was cheating. But that 33:39 is 7 minutes out of the top 100, and the best time in the top 100 is 10:44. That means about 30 seconds per challenge. FreeCell for me is quite easy most of the time (you can see all the cards before you start) and some challenges aren't very hard, even the medium ones. One FreeCell challenge tonight I did in 6 seconds. But Spider gives you no such advantages unless it is a "finish the deck" game where all cards are showing. If no cards are showing in Spider, I find it hard to believe those, along with others where few or no cards are showing, can be done fast enough to get the times that are being achieved.
Sorry for the long rambling but I wanted to share that some people can get relatively good times without cheating. Hopefully some of the ideas I mentioned above will be helpful to others to get their times down. Practice doesn't make perfect, but you can learn from it.