Do You Need A Security Clearance To Work In The Training Room?

There is no requirements to have a security clearance to handle PII (Personally Identifiable Information). It's not classified information.

PII in the military is falls under SBU or CUI - Sensitive but Unclassified or Controlled Unclassified Information and is covered under the Army's Privacy Program* and not the Army's security regulations (i.e., AR 380-5 and others in the series).

There IS a requirement for privacy act training if you are handling PII and penalties for mishandling it - reference the program for details.
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* The Army Privacy Program - https://www.rmda.army.mil/privacy/RMDA-PO-Programs-Privacy-Program.html

COL Randall C. nailed it.

If a Soldier In a clearance requiring MOS or shop loses their clearance - or has access suspended pending investigation - training room is one of the few places a Soldier can go and still be a productive member of the team. Training room, supply room, motor pool. That's pretty much it. Saw it more than a couple times working in MI.

You may be confusing security investigations with security clearance because the various Investigation levels can qualify you for a clearance if you have a “need to know”. Presumably, he accesses DTMS so he should at minimum have a favorable background investigation or tier 1 (T1) or equivalent investigation. A favorable T1 investigation can be used for a confidential clearance if the position requires classified access. T3 qualifies for Secret and T5 for Top Secret if there is a requirement.

Training records are not classified information. It is generally covered under the SBU (Sensitive but unclassified) umbrella but PII does have some added levels of protection needed. When I was working in G-6 with 3rd Marine Airwing we had a large portion of our staff working in secured areas. S-3 and S-4 was part of the small contingent of unclassified offices as they aren't handling classified material as a daily part of their jobs. It was where alot of Marines would work while pending their clearance stuff to be cleared by G-2.

No, personal information is not related to any form of security related requirements, the privacy act does apply and binds the NCO to confidentiality. He would be subject to UCMJ if he mishandles the information. There should be no classified material, or safe in a standard training room either.

Did the individual never have a clearance or was it revoked?