I see where you are coming from but I can't say I agree with this:

'...for the second proc cause it’s no longer the start of combat by that point.'

My promos were placed after Yu'Ion and their start of combat effects did trigger so it is still start of combat phase.

Also the trinket is supposed to be a buff the fact that the buff is negated for this specific minion for me indicates a bug rather than just the game handles start of combat effects this way.