Sorry for another past-due comment.  I've missed this until I actually try to
implement them from the spec.

generator-any is defined to return #t when any of the item satisfy the predicate,
but srfi-1's any returns the true value the predicate returns.  Using non-boolean
return value of any is common pattern, so I suggest generator-any be do the same.

It also applies generator-every; srfi-1 returns the last return value of predicate
if all the previous application yields true value.  (Though I see using non-boolean
return value of every is less common than any).

Wordings may be tweaked a bit.   My shot:

generator-any pred gen
   Applies pred on each item from generator gen.  As soon as it yields a true value,
   the value is returned without consuming the rest of gen.  If gen is exhausted,
   returns #f.

generator-every pred gen
   Applies pred on each item from generator gen.  As soon as it yields #f, the procedure
   returns #f without consuming the rest of gen.  If gen is exhausted, the last value
   returned from pred is returned.   
I'll send pull req for reference implementation change.