This is exactly why English is so difficult and confusing. “I’ll be home in 10 minutes” is absolutely correct. However, I have heard people use “I’m home in ____ minutes”. Any situation I have heard this is when the listener wants the speaker home (whether they miss them, need them home to do something, or if the person is “running late”) and the speaker is trying to ease the listener’s mind by wording the sentence as if they are so close that they are already home (even though they aren’t haha). I realize this is confusing, if you have any questions you can send me a message. I hope this helped 🌈

The second one is correct because the word "will" expresses future tense.

The second one is correct and would be the standard, written, adult way of saying this. The first one isn't exactly incorrect. It might be used in casual conversation, especially teenagers or younger kids. I hope that helps.