Only native coins are added to a chain by default. Tokens for that chain can be stored, you’ll just need to add them before they’re displayed. Make sure you do so from that account.
Here’s the steps. I prefer the coingecko method myself, as i always mess up something when I copy/paste: How to View Your Custom Tokens in MetaMask
There’s also the “Token Detection” feature that can be found in Experimental settings. Just be sure you know what tokens you’re interacting with when you use that feature. Random tokens you aren’t familiar with could be a potential attack vector. For example a “dust attack.” You can always just remove one from the Metamask view if you dont know where it came from.