I have a poodle and a Lagotto (a breed with a very thick, curly, double coat similar to many doodles).
I'm not a fan of the kind of brush you linked. The pin side often doesn't get deep enough into the coat to work out mats, and the soft brush side is nearly useless for curly-coated dogs (probably nice for smooth coated dogs, eg. Doberman, Whippet, Staffordshire Terrier, etc. though!). My preferred tools are a greyhound comb (a metal comb with wider teeth on one side and narrow teeth on the other) and a slicker brush that's long enough to get all the way through the coat (you don't want to be scraping the skin with the slicker, but it should still be able to get deep in the coat).
If your pup is changing coats from puppy to adult, and/or has a double coat (a coarser outer layer and a soft, downy under layer), it's pretty normal to be seeing a decent amount of hair come out! This is usually mostly dead hair that's shed or about to shed on its own, but gets stuck in the curly outer coat so can't come loose without brushing. It's a good thing to get it out, because if it stays it just gets tangled and causes nasty, painful matting, as well as traps heat. That's not to say you should be yanking it out hard - if it's ready to come out, it'll do so with firm but gentle brushing or combing. If you're really yanking there's probably a mat or tangle involving healthy, firmly attached hair that needs a different approach to avoid causing pain. Many poodle people do shave their young dogs down during coat change, unless they're planning on showing, because the upkeep is so difficult - it might be worth paying for more frequent grooming until this transition is over (around 18 months for poodles, might be different for your boy because he has golden mixed in).
For a really felted mat, often the best approach is to cut it out entirely. I like to use a pair of little, blunt-tipped grooming scissors for that, because I can slide them between the skin and the mat without risking stabbing the dog. Mats do happen with longer, curly fur no matter how careful you are, especially around the ears, armpits, groin, base of tail, and around where a collar or harness lays, so check those areas regularly and extra carefully. For tangles, work from the outside in, gently combing or brushing out the ends of the fur, then working back towards the roots. A good detangling spray is a huge help with this, and you can also pick up a leave-in conditioner to use between grooms if you need to.