So give them time off to grieve.
Once you say that “they need you [the manager] in a time of crisis” you are putting the tragedy in a work-related context. The crux of the issue is the tragedy that happened. Not how the supposed leader responds to it.
The worker bees can get space to grieve alone or among their peers.
Sometimes all that’s needed is for the manager to not be a giant fucking dick.
My aunt passed away a few years ago, and I took a few days off work to go to her funeral (a few hundred miles away).
When I mentioned that I was going to take a few days bereavement leave, my manager at the time responded by rules lawyering whether the death of an aunt qualified under the company’s bereavement policy (it did). He otherwise said all the right things, but that’s what I remember nearly 10 years later.
I came in on a Saturday to let the team know of his passing, and to work. We had scheduled a weekend hackathon—if I recall, this had been my idea originally.
My boss, very sincerely concerned, asked me, “why are you here? You can go home.” I told him there’s no where else I’d rather be. That wasn’t only because he was such a great boss, but that was a large contributing factor. He kindly, gently said he understood and that I should stay and contribute whatever felt comfortable and leave whenever that felt like what I needed. That didn’t make mourning feel any less difficult, but it made me feel like I was right that work was where I needed to be that day.
My point is not that this is the form all leadership should take. It’s true that giving people time off to mourn is almost definitely the best default. But there is a compassionate kind of leadership that can be this welcoming and compassionate comforting.
I think a lot of people still don't realize that everyone deals with emotions differently, even though they've been told that a lot in the last few decades, and perhaps a lot longer.
And yes, I agree that a lot of people have trouble recognizing different ways people process emotions. It’s been a persistent thing in my life, I’m well over in the differently column for a lot of people (ADHD/autistic).
If he had merely offered to let me go home—or, worse for me, insisted—I would agree that it wasn’t particularly noteworthy as far as compassion goes.