How to reproduce:
1. Download attached project file and open scene '1'
2. Enter Play Mode

You can see the white particle of particle system 'a' and then the black particle of particle system 'b'. Check the script 'Test 1' attached to 'Particle System'. Using simulate time 1.05s for 'a' and 'b', while 'a' has a lifetime of 1s and 'b' has a start delay time of 1s.

Actual result: PartilcySystem.Simulate has a noticeable delay. White particle blinks and then black particle shows up
Expecting result: White particle would not show on screen and black particle shows once we press the play button

Reproduced with: 5.5.5p2, 5.6.4p3, 2017.1.2p3, 2017.2.0p3, 2017.3.0b11, 2018.1.0a5