If there are no masteries or passives triggered, this is the only explanation I can share. 

First, your Deacon is slower than enemy Kymar. He just goes first in your first try because of turnmeter boost. 

Second, turnmeter in raid is not simple as many thinks. It goes something called "ticks". I can't explain how this works since it is very complicated I can't even explain it to myself lol. I just understand the concept because of years of playing this game and other game that have similar, if not the same, turnmeter "ticks". 

We don't know how many "ticks" are required to fill up a turnmeter and there are turnmeter overflows happening behind that we can not see. What I can tell you now, since you added Yoshi, which is faster than your Deacon, a turn happened before your Deacon takes a turn, means there is additional "tick" happened before Deacon's turn, where in your first try there is only one "tick" after your Arbiter moves. That is why enemy Kymar, which is faster than your Deacon steals a turn. 

So it means, your Deacon is not speed tune correctly to your Arbiter. Try putting it in Deadwoodjedi's speed calculator. First without Yoshi then try with Yoshi, you should see that the speed requirements goes up if Deacon will be third champion to move instead of being second. 

A reference for speed ticks and turnmeter overflow are explained in this video https://youtu.be/Seuw5HU_Tm8 it may not be exactly what is happening in your case but it is a great reference showing how complicated turnmeter in Raid works lol. 

I wanted to show a graphical representation of what I think happened but this is no way accurate. 

Arbiter  *Tick*  *Tick*   Deacon

*Ticks*    *Tick*  *Tick*  *Tick*     Kymar

Arbiter   *Tick*  (Yoshi   *Tick*)   *Tick*    Deacon

Each move represents a "tick" and another "tick" after a move. 

in the first line which is your first try, Arbiter boost then I put another "tick" representing that your Deacon is not speed tune. 

in the second line, showing that while your Arbiter boost turnmeter and Deacon moves, it took four "ticks" before Kymar can move and shows Deacon move first.

in the third line, showing your new team with added Yoshi, you can see that it still requires 2 "ticks" before your Deacon can move, then you added Yoshi (and a *tick) so it offset your Deacon to move after enemy Kymar.

JoinME is on the right track, there's no easy way to explain it, but the ticks get thrown off when you get other people in the mix.

Deadwood has a full explanation of speed if you really want to geek out with the math... https://www.deadwoodjedi.com/wystix-calculator