Is this type of training ok?

First off let me say that I know there are a lot of different opinions on the best training methods. I just want to make sure that the method that is being used with my dog is ok. I've never used a professional trainer before so I'm new to this.

Buttercup started her obedience training this weekend. She had two lessons, one on Saturday and one on Sunday. From now on it will be once a week (with me working with her through the week).
The trainers had choke collars that they brought and also a martingale with a chain loop. They brought all of them just to see what fit her and they used the martingale because they said they liked it better because it's easier to show people how to use the correct way. They demonstrated "corrections" with it and one trainer made me practice on a bucket filled with weights while the other trainer worked with Buttercup. They said that for every one correction you give, you want to give even more praises when the dog gets it right.

She actually did really good the first day. She learned heel and auto sit. They hardly gave her any corrections the first day, mostly just lots of praise and showing her what they wanted. When they did correct her, she didn't seem to mind it and bounced right back.
The second day was tougher.... It was just a follow up on the day before but with less room for error. There were more corrections this time (a hard upward tug on the leash). Buttercup didn't like it. She was ducking her head a little bit in a heartbreaking way. She started to "burn out" a lot quicker than the day before. They said that it was normal and that later on she won't have to be corrected hardly at all.

As soon as it looked like she was getting tired they stopped and took a fun break, running around and letting her play. She went right back to loving them.

Does this sound ok? I really liked it the first day but the second day it was almost like watching someone spank your kid.... I wanted to cuddle her. It's not like they were really being mean to her or anything, but it still made me hurt to see her kind of pouty.

They are really nice people (husband and wife) and their two dogs are really sweet and well behaved.

I just need some 2nd opinions!