I summoned a zombie and used this tag to give it speed from a command block and I truncated the command (since it is slightly too longt) and used it in chat.
summon Zombie ~ ~1 ~ {ActiveEffects:[{Ambient:0b,ShowParticles:1b,Duration:999999,Id:1b,Amplifier:20b}]}
The zombie spawned without speed, but had the speed particles. I had the zombie chase me. I then splashed the zombie with a swiftness potion and instead of giving the zombie the speed boost of the potion (level I or II) the zombie got speed 21 from the ActiveEffects. The duration from the mob being spawned was how long it lasts.
I tested this on a zombie and a sheep with various splash speed potions.
I had the zombie chase villagers as well as myself. I tested various Durations ranging from 400 - 999999, and Amplifiers from 1b to 20b. I also got similar results when I gave a zombie slowness and weakness ActiveEffects and I tossed the corresponding potion at the mob.
Did I type the command correctly?
Does anyone else have this issue?
Comments

Fixed somewhere between 15w35b and 15w44b.