Correct use of a colon in a list

Generally speaking, it's common style that if a colon is used within a single sentence, what comes before the colon should form a complete sentence on its own.

Following that style guidance, the original sentence in the question should be rephrased slightly if the colon is to be kept:

The other members made contributions: person A helped with x, person B helped with y, and person C helped with z.

Note that I also replaced the semicolons with commas, since that's the more common style choice in this particular construction.

At least with its inline use, the reason that what comes before a colon should be a complete sentences is that, if it isn't, the colon shouldn't be used at all.

From The Chicago Manual of Style, 6.67 [paywall]:

Many writers assume—wrongly—that a colon is always needed before a series or a list. In fact, if a colon intervenes in what would otherwise constitute a grammatical sentence … there is a good chance it is being used inappropriately. A colon, for example, should not be used before a series that serves as the object of a verb. When in doubt, apply this test: to merit a colon, the words that introduce a series or list must themselves constitute a grammatically complete sentence.

      The menagerie included cats, pigeons, newts, and deer ticks.
            not
      The menagerie included: cats, pigeons, newts, and deer ticks.

Taking the example sentence in the question, the inline version of it could also be written without the colon, also if it were rephrased slightly:

The contributions of the other members were person A helping with x, person B helping with y, and person C helping with z.

Style guidance for a vertical list is more relaxed—and therefore much more open to subjective interpretation. You can make it the same sentence with the same punctuation, simply separated vertically, or you can introduce a series of individual phrases, clauses, or complete sentences.

Note, too, that if it's the same sentence with the same punctuation, that means a vertical list does not need to have its introductory sentence end with a colon.

So, maintaining the punctuation, the above two inline variations of the original sentence would become the following two vertical lists:

The other members made contributions:

• person A helped with x,
• person B helped with y,
• and person C helped with z.

The contributions of the other members were

• person A helping with x,
• person B helping with y,
• and person C helping with z.

But since guidance with vertical lists is more relaxed, the punctuation doesn't need to be maintained. At least in the first version where a complete sentence followed by colon is used to introduce the list, the list items could also each start with a capital letter and end with a period, start with a capital letter and end without punctuation, or start with a lowercase letter and end without punctuation.