not sure what is in Prime, but most regular dechlorinators use sodium thiosulphate (Na2S203-).
when Chlorine is applied to tap water, it forms hypochlorous acid (HOCL-) and hypochlorite ions (OCl). The hypochorous acid is the main disinfection agent.
sodium thiosulphate reacts with this and through a reaction forms harmless Chloride ions (Cl-).
As far as the reaction time goes, I have looked for this in the literature at work and I can't find it anywhere.
at work, we used to dechlorinate using sulphur dioxide, which works along the same lines, and our contact time in the chamber was about 8 minutes. Keep in mind though, that being wastewater, we have a lot more compounds to react with chlorine (and therefor add more chlorine) and a lot more time is needed to fully react.
I believe the reaction time with proper mixing would be almost instanteous, especially given the low amounts of chlorine residual found in tap water (usually 5.0mg/L of chorine in my area, for instance).
thankfully, we don't use chlorine anymore, we now have UV disinfection - much much safer to work around