In general, there are a lot of different ways to create different sounds you just have to experiment with your technique. We can just look at palm muting and pick for now and all the different ways you can change the sound you make.
How much pressure you put on the strings when you palm mute will change the tone of the sound. Also where you palm mute will also affect the sound.
There are many, many, ways that picking can affect your sound. I'll just comment on a few.
1.First of all, what type of pick (thickness and material) will affect how the notes you pick sound. (Try to pick with a quarter to hear the difference.)
2.How hard you pick will affect the sound.
3.Where you pick will affect the sound.
4.How you hold your pick and your picking technique will affect the sound. (look up pinch harmonics for an interesting example.)
Any combination of these could result in the sound you are looking for. You have to experiment with these to get the sound you want. Your technique and how you play greatly affects how the notes you play sound. There are many other ways to change the sound coming out of your guitar but if you want to focus on palm muting and picking these are the areas to focus on. In general, the "sound" you make is dependant on your technique and there is no wrong way they just change the tone of the notes.
P.S. Whoever told you your alternate picking palm muting should not sound like it does is just being way too picky about the sound. Different guitarist just sound different in general playing the same thing and down picking vs alternative picking in general should sound slightly different.