Instances don’t “sync” with each other. When you make a post, it gets sent to a list of recipients. If your instance has someone on that list, you get the post. If it isn’t, you don’t. Which isn’t really what I understand as syncing, and it sounds like it’s not what you expected either. It’s really more like how email works.

The list of recipients usually includes the person you’re replying to, any people you mention in the post, and all your followers. On Lemmy, it includes the community you’re posting to, which then shares the post with all of its followers (subscribers).

But Lemmy users cannot follow other users, they can only subscribe to communities. And Mastodon users don’t tend to use communities. This means that the ways in which your instance can realistically receive a post are very limited:

• it mentions someone from your instance
• it’s a rare Mastodon post to a community (or reply to a Lemmy user)
• an Mbin community captured the post via its hashtags and someone on your instance is subscribed to that community

If you want to properly interact with Mastodon, I recommend switching to either Piefed or Mbin. Both of them are similar to Lemmy, but support following users, avoiding this issue.