Were you there to see how they did this? I'm no expert, but I've painted enough cabinets to know if you're DIYing, you should use a self-levelling paint, foam rollers/brushes and take the doors off the cabs. Best case scenario, they take them off and spray them in the shop after prepping them properly.

What prep and process did you agree to, and did you see samples of his work? This is not what I would have wanted.

Your post uses the word “repaint”, so I am wondering if this was the texture before it was repainted, it makes sense the texture would remain, unless the contract addressed that.

They are doing spray finish on the doors and drawer fronts to ensure a manufactured finish.

Sorry, I'm not sure I understand. Are you saying that the pictures are showing the finished product after spraying?

I wouldn't be happy with that. They could have sprayed the cabinet boxes too, they just have to use plastic sheets to make a "spray booth" to surround the area they are working on.

I want to be an informed customer and ensure we’re asking for a finish that’s reasonable.

That comes before the work starts.

What does your contract say about how the cabinets will be finished?

The contract should also specify the materials used -- the exact paint, for example.

If key is wanting to know what to expect in terms of finish, tell them your friend Daisy, a 50 + teacher and occasional DIYer says that she could have done better and knows to choose paint and tools carefully. You had expectations that, as professionals, they would have done, at minimal, the same. Tell them you realize that you will not get a factory finish by painting in house, but that what you have is unacceptable and was obviously done by a (very) nappy roller. I'm guessing they'll need to sand a bit and redo.

Lots of cabinet painters do not spray the boxes. The reasoning here is that the doors and drawer fronts are what you see. Once they are installed, the boxes are pretty much covered up. Personally, I am not a fan since you can still see the side panels. Also, this is not an issue of using a foam roller. I never use foam rollers and most professionals do not use them either. The problem with cabinet painters is that not all of them are actual painters. They might be cabinet makers who build cabinets and spray cabinets, but cabinets are easy to spray when you can lay all the pieces flat on sawhorses. Spraying the boxes inside a persons home requires more skill, which is why many will opt to roll them and have them come out looking like what you have here. Sadly, the fix is not as easy as people think. Sanding away heavy roller stipple will require some serious sanding.

If you had a smooth finish before and all they had to do was spray over the old after prepping them, there's no reason that the new finish shouldn't be smooth. What you've posted is substandard as far as I'm concerned. I've refinished quite a number in my past when I had my business. I can't think of any professional who would consider that a quality finish.

IF your cabinets were smooth before

That "orange peel effect" is unacceptable.

It looks like rolled primer or wrong type of sprayer or pressure or mix

which was not sanded to be smoothed

Primer needs to take time to dry then sand then spray.

Not an easy fix. Must be sanded back down to smooth primer then painted again.

Even IF cabinets had "orange peel" previously, A PRO refinisher/ painter would of discussed this with you & advised to strip it down & redo correctly.

The higher gloss shiny coat is not good on cabinets, either. Seeing a light glare or worse a reflection is not suggested for painted cabinets.

Also, White cabinets with wrong seal can yellow over time. Make sure they're using a non-yellowing sealer especially made for this application,too.

Here's a link to video on how to fix orange peel on cabinets

https://www.google.com/url?q=https://m.youtube.com/watch%3Fv%3DEhSg1kuL_4M&sa=U&ved=2ahUKEwitioTFofrgAhUj1VkKHU4fCAwQtwIwAHoECAkQAQ&usg=AOvVaw0c_k-g_IYY9Qk31fmx4WNi

A satin finish is a more updated look.

Ask them if they are using a self leveling paint, that is actually meant for cabinets. If they are not using that, you might want to ask them to use that.

Here is how I would expect a Pro cabinet finisher to spray paint kitchen cabinets. A brush painted amateur job would differ slightly in that you wouldn't hang the doors to paint. You'd place them on a work table or easel instead. It's time intensive work, and should take 7-14 days to accomplish completely and cost between 5--9K depending on kitchen size and amount of detail in cabinets.

Remove doors and drawer fronts. Number on an edge to locate their home easily.
Remove hinges and hardware.
Clean with TSP (tri-sodium phosphate)
Rinse (required) and let dry.
Scrape any loose finish.
Fill any damaged spots or hardware holes that won't be reused.

Fill oak grain with PorePac if you want a smooth finish then sand. Repeat. (Or just buy new cabinets. The labor to donthst is insane.)
Sand fill smooth.
Scuff sand the rest.
Tack off dust.
Hang in dust free paint booth with wires through hardware points.
Tack off dust again.
Spray with alkyd based primer like BIN.
Scuff sand again.
Tack off dust.
Spray with second coat of primer.
Spray with first finish coat of post catalyzed conversion varnish. Amateurs can use an oil modified waterborne enamel like Cabinet Coat.
Spray with second coat.
If glazing is to occur, that is next.

Add more molding or decorative details to boxes, filling nail holes and sanding smooth.

Repeat prep process with face frames and exposed cabinet sides using plastic to create a spray booth on site. If interiors are to be done, they are done before face frames and sides. Interiors are difficult, and add both time and expense to the job.

Allow everything to fully cure.
Clean hinges and hardware and clear coat if you're keeping the old hardware.
Install new (or old) hinges and hardware.
Re-install doors and drawers and adjust for proper clearances.

If you are receiving a job without this amount of effort, or these professional products, then you are not receiving a quality professional job.