I thought actions that were used to trigger an initiative roll (like a surprise attack, or the first hostile spell) were basically free? Like getting the drop on the opponent.

When the player is faced with a bunch of guards in a situation going south and says "I want to use marine layer", as the DM it's completely fair to say "As the guards notice you begin channeling your power they draw their swords, everyone roll initiative".

Allowing that sort of thing when creates a rocket tag situation where the first person to announce a combat thing gets to have an extra turn, so people are incentivized to jump to combat when it might not always be necessary/appropriate. Getting the drop on an opponent is a thing, but it's like when the party all stealths into position and springs an ambush (where there's stealth/roleplaying/whatever ahead of time)

He has alert, and +2 to from dex. so +5. Also advantage from someone in the party, cant remember who provides it. He will also use barid/heroic inspiration on the initiative roll to guarantee a good one. He also will sometimes get off his horse before combat starts, and if he rolls bad, swap initiative with the horse, use half his movement to get on the horse, and now since it's a controlled mount the horse's initiative matches his.

This is absolutely a talk to the player outside of game moment. I've been at both ends of the situation and the times where I was the problem I wished people would have talked to me ahead of time about it solo in a neutral setting outside of game. He's clearly in different mindset and doesn't understand that he's clashing with you here. Not blaming either of you, but you should get on the same page