Speaking as a systems consultant, I see several things wrong with this interaction. In no particular order:
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Time is money and volunteering is for retirees with nothing better to do. Invoice for your work at the market rate. ALWAYS. Discount if you feel the need, but always let them know you cut them a deal at your option.
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You didn't mention much in the way of communicating with the staff. If there was even a remote possibility of an outage, that should have been communicated.
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People can work around outages as long as they know they're coming. It's when shit goes down unexpectedly that people get angry. I seriously doubt there was a "no downtime" expectation. Instead I suspect it was a matter of timing and the interruption impacted a deadline. Also, not everyone employed by every church is on-site all the time. Is it possible the staffer made a special trip in to accomplish something?
So, yeah, from where I'm standing? Looks like some fault on both sides.