You are correcte in noticing that "ton" is the masculine form while "assiette" is feminine. This apparent mismatch is due to the word assiette starting with a vowel. "Ta assiette" would have two vowels clashi g in a difficult to pronounce combination. The French take the simple way out and use the masculine form whenever this happens.
"Mon amie" is another example. "Amie" is female but you use "mon" nonetheless I believe there is a dedicated lesson on this.
Chris is right there, you can see the related lesson:
However, I also agree this example is a bit complicated and misleading at this level, so I've decided to replace it with a more straightforward sentence.
Merci et à bientôt !
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