Some quartets (in at least one circumstance) indicate a natural leader, in which the other players subtly adjust tempo and pitch to the leader's cues. In other quartets, there's no such indication, and all the players adjust to each other. Fascinating stuff.
(This one's for Mom & Dad.)
Most interesting. Of course, as pointed out, the first violin is the traditional leader. The tempos would have been agreed upon during rehearsal. “Brain freeze” can occur during a concert and then the goal is to come back together. It is not “my way or the highway” . The goal is then to come back together without breaking down. One learns how to make adjustments almost without thinking about it especially when playing in the same ensemble for many years. As for intonation, that is always a matter of listening. Again, one learns to make the adjustment almost without thinking about it. The music is the important thing, not the ego.