Phoenix powers: a blessing or a defeat

This is my First NG+, I've done a regular run previously and right now I'm at post Phoenix Gate remembrance, where I Just got Ifrit powers (not really, NG+) but something let me thinking.

What is the true source of Clive having Phoenix powers? Are they from Joshua willingly giving Clive part of his powers when he was a kid who has never primed before and who struggled to use Fire++ (his gameplay on Phoenix Gate makes him tumble when casting)? Or the true origin for Clive's powers is actually the fact that Clive beated Joshua in the events of Phoenix Gate and forcibly absorbed part of Joshua powers?