Handling the conversation.
FIRST, ESTABLISH THE FACTS
Was it a server problem, their site, or their own change?
Frequently it is the third, and the client does not realise.
IF IT WAS A SERVER PROBLEM
Say so plainly, without excessive blame.
"The server was affected, it has been resolved, here is what happened."
Clients accept infrastructure problems. They are less forgiving of evasion.
IF IT WAS THEIR SITE
Say so kindly. "The plugin update caused it, I have rolled it back."
Not "that was your fault".
IF IT WAS THEIR OWN CHANGE
Handle carefully. Fix it, explain what happened factually, and suggest a backup before future changes.
WHAT NOT TO DO
Blame the provider reflexively. It suggests you have no control over what you sell. Absorb blame that is not yours, which invites more. Argue.
THE POSITION TO TAKE
You are the person who resolves things, whatever caused them.
That is what they are paying for, and it is a stronger position than apportioning blame.