correct.js

function createUser(username, callback) {
    var connection = DatabaseClient.connect();
    var users = connection.call('collection', 'users');
    var query = users.call('query', {username: username});
    return query.then(function(existing){
        if(existing) throw new Error("User already exists: " + username);
        else return users.call('create', {username: username});
    }).fin(function(connection){  return connection.call('close'); });
}

es7.js

async function createUser(username, callback) {
    
    var connection = await DatabaseClient.connect();
    try{ 
        var users = await connection.collection('users');
        var query = await users.query({username: username});
        if(query){
            throw new Error("User already exists: " + username);
        } else {
            return await  users.create({username: username});
        }
    } finally {
        connection.close();
    }
}

original.js

function createUser(username, callback) {
    return DatabaseClient.connect().then(function(connection) {
        return connection.collection('users').then(function(users) {
            return users.query({username: username}).then(function(existing) {
                if (existing) {
                    callback("User already exists: " + username);
                } else {
                    return users.create({username: username}).then(function (user) {
                        callback(null, user);
                    });
                }
            });
        }).fin(connection.close);
    }).catch(callback);
}

I would have written it this way:

// Return a promise not call a callback, seriously!
function createUser(username) {
    var connection = DatabaseClient.connect();
    return connection
        .then(function(connection) {
            return connection.collection('users');
        })
        .then(function(users) {
            return users.query({username: username});
        })
        .then(function(existing) {
            if (existing) {
                throw new Error("User already exists: " + username);
            }
            return users.create({username: username});
        })
        .fin(connection.close);
}

async function createUser(username, callback) {
    const connection = await DatabaseClient.connect();
    try {
        const users = await connection.collection('users');
        const query = await users.query({ username });
        if (query) { throw new Error(`User already exists: ${username}`); }
        return await users.create({ username });
    } finally {
        connection.close();
    }
}

@sukima nice, that also works

@abrkn nice, I really should use const more.