When you say technician who are you talking about?

You need an electrician to come check the wiring. It is most likely the outlet is running on the switch. Not sure why or how it would have worked before without looking at it.

There are two ways to use an outlet(duplex) for that use. One is to wire one plugin to the switch and the other hot all the time. That needs to be done during install, the wiring connections are a bit different.

The other is how I did the same situation(dishwasher and disposer) in our current home.

I plugged the dishwasher into the bottom socket and an air switch into the top socket. The disposer is plugged into the air switch plug adapter. There is a flexible plastic hose from the air switch adapter to a flush mounted plunge type button mounted in a hole in the sink. (Our sink is stainless and I had to drill another hole on the opposite side of the hand soap dispenser).

The dishwasher is on all the time(when the controls are used) and the disposer is only on when the plunge button us pushed---once for On and a second time for Off.

In your case, use the receptacle for the purifier and an air switch in the other socket for the disposer.

I've wired outlets so that one is hot constantly and the other is switched. If you were running this way before, then yours must be wired the same way.

Did you by chance unplug the purifier when the fuse blew and then plug it back into the other receptacle?

Swap the plugs and see if it goes back to the way it was.

FWIW it's pretty easy (and not uncommon) to wire a dual outlet to have one switched and one hot all the time. For example, I do it for the bedroom light with a clock radio plugged onto the same outlet. (need continuous power to the clock but want to switch the light on/off).

I'd question your technician's ability.

FWIW, I was not familiar with an "air switch" so I googled it. Here's a link to one.
Insinkerator air switch

Pretty neat but if the OP already has a switch then why bother.

There is a linkage on the side of the outlets between the screws that if broken you can wire each outlet on a separate circuit. But if she swapped how they were plugged in, then the disposal would be on all the time when she plugged it in. I am not thinking we are dealing with that scenario.

Still need the wiring and outlet looked at so we know what is actually going on.

Just confirming it is possible. My dishwasher and disposal use the same outlet.

Did someone change out the receptacle under the sink? Newer codes require that receptacle to be GFCI protected. If they installed a GFCI receptacle, it can not be split wired like it was before without adding another receptacle down there, or putting the GFCI in the breaker panel.

If the duplex receptacle had been wired with one position on all the time and the other switched, and the plugs were swapped, I'd expect that now the disposal would run all the time.

Is it possible that the disposal actually has its own internal switch? That would explain things.

In any case, I agree with the advice to try swapping the plugs before doing anything else.

PS - you might want to consider posting this in the Wiring Forum.

You need an electrician.