Terence, what method are you using to connect your site to Mastodon? Are you using Bridgy Fed, Activity Pub, or something else? Some of these have different methods for pulling in backfeed. I understand that Brid.gy also recently added backfeed from Mastodon as an option, so if you’re using that for your Twitter responses, it should be relatively similar.
Another thing to check is to make sure they’re not somehow going into your spam or trash folders if you’ve got anti-spam bits turned on.