How to be assertive as a PM without being seen as authoritative? How would you address this issue?

During a recent 360° feedback review, I got a comment that stuck with me.

My communication can come across as too strict.

I guess it was tied to a specific situation: team member were repeatedly late to stand-ups, and I addressed it very directly in front of the whole team. Maybe I was just not in a good mood because other issue going on and waiting 5 more minutes with other team members for the last one (because he was on a coffee break and forgot about standup) was the last drop for me.

I don't clearly remember words I used, but the idea was something like "We are all waiting just for you, pls be respectful to others and be punctual next time".

From my perspective, it was a simple issue - respect people’s time. But the way it landed was different and resulted in receiving a negative feedback for yearly evaluation with my superior.

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From my perspective, as PMs, we’re expected to step in when things don’t work.
If people are late, misaligned, or blocking others, doing nothing is not OK. Being assertive is part of the job.

If you avoid being “too strict,” you risk the opposite problem - things slide. I have a feeling that in the IT world people can be quite sensitive to this type of communication.

How would you address the issue?