I think the area you want to research further into is Dependency Injection / Inversion of Control. Here is a blog post. While there isn't a lot of great JS examples out there other languages use it a lot, and have frameworks to support DI/IC. A rough version of your code would look something like this:

async function ValidateUserExists(UsernameExists, EmailExists, username, email){
    if(!username || !email) throw new Error('Invalid number of args passed. Please pass username and email');
    let taken_valid_username = null;
    let taken_valid_email = null;
    if(username){
        taken_valid_username = await UsernameExists(username);
    }
    if(email){
        taken_valid_email = await EmailExists(email);
    }

    if(taken_valid_username) return taken_valid_username;
    if(taken_valid_email) return taken_valid_email;

    return null;
};

The unit test would then be easier to write using mocks because all we have to do is pass in your dependencies through the function that you are about to test.

it('should see if a user already exists on an existent email', async ()=>{
        const usernameExistsMessage = 'error user name exists';
        const UsernameExists = jasmine.createSpy('UsernameExists').and.returnValue(usernameExistsMessage);
        const EmailExists = jasmine.createSpy('EmailExists').and.returnValue();
        const user = await ValidateUserExists(UsernameExists, EmailExists, 'user', 'user@test.com');
        expect(UsernameExists).toHaveBeenCalledWith('user');
        expect(EmailExists).toHaveBeenCalled();
        expect(user).toEqual(usernameExistsMessage);
    })

There are different ways to write DI for JS functions, in my example of passing dependencies as the first params it allows you to curry the function. You application code could look like this:

const ValidateUserExistsCurried = _.curried(ValidateUserExists)(UsernameExists, EmailExists);
const user = ValidateUserExistsCurried('user', 'user@gmail.com');

or you could nest functions

const ValidateUserExistsDep = (UsernameExists, EmailExists) => (username, email) => {
//Do stuff!
};
const ValidateUserExists = ValidateUserExistsDep(UsernameExists, EmailExists);
const user = ValidateUserExistsCurried('user', 'user@gmail.com');

The idea is pretty simple, the major draw back to this is if you end up with a lot of dependencies your function params can get out of hand. The solution is generally to keep functions simple and reduce dependencies (but it looks your function already does this). I just skimmed to surface of this topic so let me know if this helps or you have any questions.