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No server holds your messages.
When both devices are online, a message goes straight from yours to theirs. There is no server in the middle to store it, because there is no server in the middle at all.
When the other person is offline, the sealed message waits in a mailbox — and only there. It is deleted the moment their device confirms it arrived, and it expires after fourteen days if nobody ever collects it.
Whoever runs that mailbox can see that a delivery happened. They can never see what was said, or read it later, because they never had it in a readable form in the first place.
One exception on the server side: a mailbox can be configured to offer an opt-in directory, so that people who do not yet hold each other’s contact card can find one another. If you put yourself on it, the operator holds the label you typed until it expires. It is off unless it is switched on, twice — once by the operator and once by you.
And one thing that leaves your device without touching a server at all: with local discovery switched on, Nex announces itself on the network you are joined to, so two devices in the same building can find each other. The announcement carries no name, no account and no key, and the value in it changes every fifteen minutes — but it does carry your device’s address, so anyone listening on that network can tell a Nex device is present. It is off until you turn it on.