The Kitzur Shulchan Aruch writes in Siman 19 Halacha 9, that if one began his Shemoneh Esrei on the first night of Pesach and he accidentally began saying a weekday amidah and he came to the Bracha of barech aleinu, that he must complete it and he is to say “vsen Bracha” because the congregation is not saying “tal umatar” - if however December 4/5 fell on a Friday night and once again he said a weekday Shemoneh Esrei, KSA again says “vsen Bracha” because the congregation is not saying “tal umatar” as of yet. Aren’t these 2 halachos in contradiction with each other, as if with Pesach he holds that the person changes early his recitation to "vsen Bracha," even though the congregation hasn’t changed yet, why not the same on Dec 4-5 that falls on a Friday night - why not change to vsen tal in a similar fashion?
My understanding of the Kitzur's ruling is that the default (or 'null' - hat-tip @Double AA) state is to recite v'ten bracha. V'ten tal umatar is a mandated addition to the amidah during a certain season. (See this question and its answer for support for this assertion.)
The season starts the first weekday arvit on or after December 4th/5th (in the Diaspora) and extends until minchah of erev pesach.
Thus, if December 4th/5th falls on shabbat, the season does not begin until after shabbat, and one would not add v'ten tal umatar on that shabbat.
Conversely, at arvit of the first night of pesach, the season is already over, so, again, one would not recite v'ten tal umatar.
I think that the Kitzur's references to the recitation of the tzibbur is his way of ascertaining whether or not one is currently in the v'ten tal umatar season.
The words of the KSA are:
טעה במעריב ליל ראשון של פסח והתפלל תפלת שמונה עשרה של חול, ונזכר לאחר שהתחיל ''ברך עלינו'', שהדין הוא שצריך לסיים כל אותה ברכה (כמו שנתבאר לעיל סימן ע''ו), אינו אומר ''טל ומטר'', כיון שגם הציבור אינם אומרים.
Extended paraphrase, following the explanation of the Chochmat Shelomo. If he made a mistake at the first night of Pesach and did pray the prayer of Chol. And he realizes his mistake but is already reciting the Birkat Hashanim, he must go to the end of the Beracha (as explained in Siman 76, that the berachot of Yom Chol are not off topic on Shabbat, but Chachamim wanted to lighten the text in honor of Shabbat). So when he is in the middle of the blessing, he must be careful not to say "veten tal umatar", because the congregation already ceased to say it for this year.
ואם חלה השאלה (הוא יום התחלת לשאול טל ומטר) ביום שבת, וטעה והתפלל של חול, והתחיל "ברך עלינו" גם כן, אינו אומר "טל ומטר", כיוון שהציבור עדיין לא התחילו. והיחיד נגרר תמיד אחר הציבור.
If the same problem occurs on Shabbat who is the first they should have say "veten tal umatar" if it had been possible, he must not say tal umatar because the congregation did still not started to say it.
The logical trick is that stop mentioning this word comes automatically, but start saying these words is a collective act.