What type of culture did you use (i.e. cup of buttermilk or freeze dried culture)? Did you check the ph before adding the rennet? How long did you Stir the rennet?
The way you described the milk behaving as you stirred the rennet, I would venture to guess that (1) the milk was fairly acidic when you added the rennet, which made the transition form the enzymatic phase of the rennet (i.e. the enzyme "clipping" off the surface of the casein), to the coagulation phase almost immediate. 2) you stirred the rennet too long for that particular condition. The stirring helped the clipped off caseins come together faster.
Normally, depending on the batch of milk, the rennet should not be stirred for more than 20-30 strokes of up and down motion (for 1 gallon milk that should be sufficient to evenly distribute it).
If you did use freeze dried culture, then I would guess that the milk itself was too acidic before you added anything to it.