Unless I’m misunderstanding I think the only case where Tweets from non-list members will appear in a list widget is when a member of the list explicitly retweets them.
One solution would be to ask your members not to do so. Another option might be to construct a search query including your list members, but also adding either
NOT @blockeduser in the query to blacklist mentions from your unwanted users, or excluding retweets from the search altogether.
Finally, you could also use our newly launched Curator tool (https://curator.twitter.com), which can ingest all Tweets from members of a list and generate a collection. In this case you’d effectively be moderating every Tweet that came through the main stream and only adding the Tweets you want to see to the output, which can then be embedded using the same widget you use today.
Each of these options has a downside, but hopefully one might work for your case. Let us know how you get on.