First of all, please note that when you activate the Phylach, you will receive bonuses only from those Skills which you assigned to the active Skill slots.
In the Phylach tab you have up to 6 unlockable slots, in each one of which you may select 1 Phylach Skill. Once you activate your Phylach, the selected Skills will start providing you with the appropriate bonuses.
Also, please note that percentage based Phylach Kills, that accelerate your Agreement upgrades, building upgrades and troop training process, actually increase the upgrade/training speed, rather then cutting off certain percentage of time.
When you activate your Phylach with a unit training speed bonus applied, all your training queues remaning time will be recalculated with your new training speed taken into account.
For example, let's say it takes 2 hours to train 100 Swordmen, then your normall training speed is 50 Swordmen/hour. with the 20% Phylach bonus active, you training speed will increase to 60 Swordmen/hour, so with the Phylach bonus activated, it will take only 1 hour and 40 minutes to complete the same 100 Swordmen training.
On the other hand, if the Phylach bonus expires before the training queue is complete, the time needed to traing the remaining units, will be recalculated once again, with the decreased speed now taken into account.
The exactly same principle applies to the building upgrade process. While the Phylach bonus is active, you building will be upgraded at a higher speed, letting you complete certain % of the upgrade (let's say 70%) faster than you normally would, but once the bonus expires, the time needed to complete the remanining 30% of the upgrade will be recalculated once again.