@Todd Baumann members should receive notifications only when they're watching (subscribed to) a card, list or board, unless they're mentioned in a comment or added/removed to/from a card or a board:
https://help.trello.com/article/793-receiving-trello-notifications
If you're receiving notifications in addition to this you may be experiencing the same issue reported here:
Which appears to be a bug ... can you clarify if that's what you're referring to?
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