I set the Twitter connection settings to “post” but my Air Tweets will not appear on Liveview.

In the versions older than 2.2.x, Air Tweets will be shown on your Liveview only when you have your Twitter connection settings on “view”.
Please change your settings from “Post” to “Browse” to see your Air Tweets. iPhone Settings > Sekai > Twitter Sync > Browse.

NOTE: In the version 2.3.0 and later, Air Tweets will be always shown on your Liveview.