What can cause honey to crystalize quickly?
Crystallization involves two stages: nucleation (the formation of the crystals, either spontaneously, influenced by solids like the walls of the container or a foreign substance, or influenced by existing crystals) and growth (where the size of crystals increases from microscopic).
Nucleation is most likely to occur when there are impurities in the honey around which crystals can form, or there are existing crystals of honey (which may be very small). Impurities could be introduced from the air or more likely on a spoon or stirrer, and existing crystals can easily form on the walls of the container or at the opening. Stirring brings these into contact with more of the rest of the honey, enabling more nucleation to take place.
As for the growth rate, my instinct is that this will depend in a complicated way on factors like the specific composition of the honey, the temperature, air pressure and perhaps even humidity of the surrounding air. In your case, it seems that the conditions were perfect for secondary nucleation and crystal growth, so as soon as an initial crystal appeared the whole jar quickly crystallized (similarly to how supercooled water will freeze suddenly when nucleation is triggered).
In terms of your second jar of honey, all I can recommend is:

make sure you use a clean utensil (preferably made of something with a smooth surface like metal rather than wood)
try not to let honey that you have spooned out rejoin the rest of the honey in the jar (in particular, if your spoon has been sitting out of the jar don't put it back in)
insofar as you have control over the temperature, don't do the whole exercise while the honey is especially cold
if you do notice any crystallized/dried honey around the rim of the jar, clean it off with a damp cloth rather than let it mix with the liquid honey

It's also worth saying you can get crystallized honey back to a liquid state by heating gently (I use a microwave for short bursts; be careful as it can get very hot and remains sticky – you do not want to get it on you!); because of the residual crystals on the container it tends to crystallize again within a few days but it's useful when you need it.