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Usually, they do. Creator pages with tropes aren't as common, but it's useful for troping trends or works that don't have enough content for their own pages. It's fine for a creator page to not have tropes.
Thing is, creators can have tropes about their works, but usually is avoided tropping creators because it may fall in tropping the person behind it, which is a no-no.
Right now a diligent troper is tropping Isaac Asimov and his work, and is doing a nice job, but there is an entry on Pervert Old Man that needs to be erased for a reason.
To win, you need to adapt, and to adapt, you need to be able to laugh away all the restraints. Everything holding you back.
Yes, I know. No troping the RL person, no tropes about individual works with pages, no audience reactions... that can leave very little things to add.
Ultimate Secret Wars
Well, if we treat them like a body of works, then "Multiple works by this creator use these tropes:"
Is a possible option, since I've done similar for serieses of works.
Disambig Needed: Help with those issues! tvtropes.org/pmwiki/posts.php?discussion=13324299140A37493800&page=24#comment-576
To explicitly answer the OP: no, they don't need tropes.
And, as others have pointed out, any tropes on a creator page have to be about their works, not about them as a RL person.
Or about them as a creator, such as those tropes listed on Creators.
According to Creator Page Guidelines, a page about a creator can have tropes that show up in many of his creations (but not from individual works) and trivia items. But do they need it? Can a creator page have just a brief description and a list of works, and be done with it?