Episodes were aired out of order, so it's not entirely obvious what happened.
Episode 1x06, Summer of Love, was intended to be episode 1x02. At the beginning of this episode, we see Quinn reopen the vortex so that he and Arturo could go through - he had control at that time, as you suggest.
However, due to that slide, the timer was damaged. There's a subplot in the episode about Quinn trying to fix it, and a very important scene was cut because of shifting it to later in the season (From the above link, bolding mine):
Counting each part of the pilot as individual episodes, Summer of Love is sixth with respect to the sequence the episodes were originally aired in on Fox, and third with respect to production order. There was a missing scene from the episode that explained the way the timer worked. According to this scene, after the first time the timer had been reset, the sliders did not need to slide at the moment the timer hit zero. However, since the timer had been damaged when Quinn opened the vortex on spider-wasp earth when the timer was weak, it could now only be activated at a unique window of opportunity, which the timer counted down towards. This amount of time could vary between a few minutes to several months. If they did not slide at this window of opportunity, there would not be another window of opportunity for another 29.7 years. This scene would have made sense if it aired immediately after the pilot. However, if it [the episode] were sixth in sequence it [this scene] would not make sense, because in the other episodes, the sliders had to slide at the specific point of time in which the timer counted down towards.
The timer counts down to this window of opportunity because that's how Quinn reconfigured it during this episode.
In short, it's yet another "blame Fox for screwing with a good show"...