You‘ll see those new gains on muscles that you recently started to train, so yes you‘ll get newbie gains with your glutes if you‘ve never done glute workouts with weights.

I assume you would see newbie gains in your gluteus maximus as well. If you‘ve been working on building your gluteus medius it‘s very likely that your gluteus maximus has received some form of stimulation since it‘s impossible to 100% isolate one single muscle. However, depending on what type of exercise you‘ve been doing, the stimulation might have been too little to have a very huge impact on your gluteus medius, so you will probably see relatively quick changes as well

When I first started doing full body workouts in the gym 3 times a week I probably noticed some gains within 2 weeks