When a field is created the skill/burst that uses it is put on cooldown the moment it's created, and its duration isn't extended by hitlag. All field skills will tick and grant all benefits to eligible units on one second intervals from the start of the cooldown. Bennett Q for example, has a 15 second CD, so the next ticks of his field are at: 14.0 remaining CD, 13.0 remaining CD and so on.
CDR and effects that increase the linger duration have no effect on the schedule of ticks. Leaving and reentering the field will not grant you a tick of the buffs immediately, they must wait for the next tick interval to obtain the buffs. The same is true on swapping characters. Some fields have particular quirks about them however.
An additional tick of attack gives Bennett the attack bonus before the Inspiration Field is fully cast.
Chongyun’s field works identically to most other fields in regards to leaving and reentering. However, here swapping between characters will apply his infusion to the new unit instantly in addition to the normally scheduled ticks.
Diona's Drunken Mist will leave a field that grants its Elemental Mastery bonus or any Healing bonuses from artifacts immediately upon swapping, separate from the healing tick.