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Dear respected Michele Marsburg,
Good morning! Thanks for posting in the Microsoft Community. We are happy to help you.
I'm sorry that you're having a uncomfortable experience using the Term Set feature in SharePoint document library that only after a refresh will the added terms appearing in the correct place and able to be applied, and from the situation you've encountered, we deeply understand the inconvenience caused and apologize for it.
According to your description, I understand your concern and I would like to collect more detailed information to better investigate the scenario, and in order to protect your privacy, I just sent you a private message, please access the private message by clicking this icon.
I appreciate your patience and understanding, and I appreciate your time and cooperation.
Sincerely
Mia