1st off, this is not something that can be asked here, not enough details, etc.

Decks are usually designed to carry 50 LB PSF live/dead load, depending on local code requirements.

Average hot-tub 6-7 people, 300-400 gallons of water, tub weight, you're looking at 95 LB PSF.

I wouldn't go by it should or it shouldn't; everything is based on load calculation and lumber spans, and that will tell you if you need additional footings, extra columns, etc.

Therefore, your best bet is to get someone who can do all that for you so you sleep well at night, or enjoy your hot tub with friends and family without anyone going to the emergency room.

Someone probably also told these people your deck should have been OK to put a tub up there, I guess it wasn't.

Good luck

Consult a structural engineer.

It will be fine.

I would consult a structrual engineer. This is not something you want to be wrong on.

Looks like that’s a MasterSpa. I noticed the orange Ecopure filter.