If an effect refers to a “[subtype] spell,” it refers only to a spell that has that subtype. For example, Knights' Charge is a card with “Knight” in its name and benefits Knights, but it isn't a Knight card.

Worthy Knight's triggered ability won't trigger when you cast it because it's not on the battlefield yet.

Worthy Knight's ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered.