If you choose to publish to "Teams", it means that player responses are share amongst the team members.
If you want all team members to see the same Twitter feed then you should publish tweets to Teams. This is only possible for Injects and Also Publish content.
If you publish Twitter content to "Player" via an Inject, all players will see the tweet but each player has a local copy, not a single shared copy. Hence should a player reply to such a tweet it will not be seen by others.
Msngr Channel example
In most channels (except Twitter), when asking for a team decision, it's expected that only one person in the team will reply. Therefore, there's a separate branch for other team members who reply after the first person.