My player wants to cast multiple charges of magic missile from a wand

So I was GMing for the first time my custom Pathfinder campaign, and my Rogue uses a wand of magic missile with 8 charges left in it against the last opponent of the session, and vaporizes him. I instinctually said he couldn’t do that, and he explained that he only needed to make his Use Magic Device (UMD) check to use the wand (which he succeeded) and he’s using the wand, not the spell, so he can use multiple charges in the same turn with the same check. It was the end of the session so I didn’t want to bog us down with an hour long rule check, so I allowed it and my villain was vaporized by the remaining 8 charges (we are low level still). I’ve been searching for a ruling on this all afternoon yesterday and this morning, and just cannot find a definitive answer.

My reasoning is: Activating a wand

Wands use the spell trigger activation method, so casting a spell from a wand is usually a standard action that doesn’t provoke attacks of opportunity.

(We are in agreement here)

Spell Trigger Description:

Spell trigger activation is similar to spell completion, but it’s even simpler. No gestures or spell finishing is needed, just a special knowledge of spellcasting that an appropriate character would know, and a single word that must be spoken. Spell trigger items can be used by anyone whose class can cast the corresponding spell. This is the case even for a character who can’t actually cast spells, such as a 3rd-level paladin. The user must still determine what spell is stored in the item before she can activate it. Activating a spell trigger item is a standard action and does not provoke attacks of opportunity.

(He still agrees with me up to this point)

UMD Description

Use a Wand, Staff, or Other Spell Trigger Item: Normally, to use a wand, you must have the wand’s spell on your class spell list. This use of the skill allows you to use a wand as if you had a particular spell on your class spell list. Failing the roll does not expend a charge.

So magic missile is now as if it were on his class list. Magic Missile has a casting time of “1 standard action”

My understanding here is, is that you can only cast once per standard action. It would be the same in my mind, a wizard preparing magic missile 3x in one day, and expending them all in one turn just because he channeled the magic missile.

Neither of us can find anywhere it say that only 1 wand charge per round, and that is what I think his hangup is.

What stops someone from making a wand of magic missile and use all 50 charges from one turn on the next boss we fight?