Can a Tentacle Rod be used with Extra Attack?

In a recent game our Monk used a Tentacle Rod to attack three times (per its normal use), then used his Extra Attack to attack three more times, then used his Bonus Action to deliver an unarmed strike. For a total of 7 attacks every turn.

Is this, as I believe, an incorrect reading of the rules?

My reasoning for attacks 4-6 are that the Tentacle Rod states (it’s long because I’m trying to be thorough):

While holding the rod, you can use an action to direct each tentacle to attack a creature you can see within 15 feet of you.

(Emphasis mine.) It doesn’t say Attack action, it says an action, and I would say that, since it specify an Attack action, and the Rod is a magic item that isn’t a weapon, that the action would be "use an object"

By the same token, the Monk rules state:

When you use the Attack action with an unarmed strike or a monk weapon on your turn, you can make one unarmed strike as a bonus action

If the action isn’t an Attack action, then the Bonus Action cannot be used for an unarmed strike.

This would mean that the Monk can get either 3 attacks with the Rod, or take his standard Attack, Extra Attack, and unarmed strike, which is still 3 attacks.

This is how I read the rules. Also, getting 7 attacks at 5th level seems to break action economy, but that’s more of a "sniff test" that a rule I can actually point to.

I found this question from a year and half ago asking basically the same thing, but about Multiattack. However, Multiattack and Extra Attack aren’t exactly equivalent, neither are PC actions and monster actions, so I’m inclined to think it doesn’t apply.

Thank you.

P.S. I’ve seen this player make similar mistakes to his detriment, so I’m pretty sure any mistakes here are 100% accidental.