Tl;dr The term is first used in the 11th century, (well before the State of Israel, or Satmar) and becomes more popular through the centuries. It is first used to refer to overtly miraculous acts designed to lead people to sin. Later it is used to refer to non-miracles, or to miracles disguised as non-miracles which bring people to sin. The Talmud refers to Satan causing problems, but does not use the exact term "ma'aseh Satan". (This based on the survey I have done, some of which is presented below. I might of course have missed some usages. If any are found which affect the above chronology, please alert me).
Rashi to Exodus (32:5) writes that the golden calf was imbued with a lifelike spirit, as a ma'aseh Satan:
וירא אהרן - שהיה בו רוח חיים, שנאמר (תהלים קו כ) בתבנית שור אוכלא עשב, וראה שהצליח מעשה שטן,
And Aaron saw: saw that it had a spirit of life, as it says (Psalms 106:20): "with the likeness of an ox eating grass". And he saw that the ma'aseh Satan was successful.
Here we see a miraculous act being described as an act of Satan. The context is clearly insidious; an attempt at getting the Jews to sin. This is not a case of a seemingly natural act. Rather, like the modern usage in reference to the (perceived) miracles involved in the formation of the state, they are attributed to malignant forces leading to sin, rather than stemming from a positive act of God.
An example of the term used to refer to something seemingly natural, is found in Maharal's Tifferet Yisrael (ch. 48) in reference to an aggada in Sanhedrin (107a) about David and Bathsheba.
וכן דוד, היה זה מעשה שטן, וכדאיתא בפרק חלק (סנהדרין קז א).
The story depicts the Satan causing seemingly natural events to lead David to sin:
And he walked upon the roof of the king's house: and from the roof he saw a woman washing herself; and the woman was very beautiful to look upon. Now Bath Sheba was cleansing her hair behind a screen, when Satan came to him, appearing in the shape of a bird. He shot an arrow at him, which broke the screen, thus she stood revealed, and he saw her. Immediately, And David sent and enquired after the woman. And one said, Is not this Bath Sheba, the daughter of Eliam, the wife of Uriah the Hittite? And David sent messengers, and took her, and she came unto him, and he lay with her. (Translation).
Similarly, Rama writes a responsum (#125) about a famous case where he officiated a wedding on Shabbat. In this incident, the bride's side was supposed to provide a dowry, but as Friday, the day of the wedding, drew to a close, her side failed to provide the full dowry. The groom stubbornly refused to proceed, without the money. And this ma'aseh Satan was successful, until the groom finally agreed to marry her, at which point Rama officiated the wedding to end the embarrassing episode, even though it was already Shabbat during which weddings are generally forbidden:
והצליח מעשה שטן עד שהגיע הזמן הנ"ל שהשוו עצמן ונתרצה החתן ליכנס לחופה, ושלא לבייש בת ישראל הגונה קמתי וסדרתי הקידושין בזמן הנ"ל
In this case, as in the usage of Maharal, the act of Satan refers to a seemingly natural series of events, that nevertheless have a sinister undertone. In Maharal's case, there was an actually supernatural event (a magical bird), whereas in Rama's case, no laws of nature were apparently violated, but a series of events nevertheless led people to sin (by embarrassing the bride), which he terms "ma'aseh Satan".
A similar usage of a similar expression is found in the Talmud (Megillah 11b). It describes Satan coming to Ahasuerus's party, and "dancing among the guests", leading to Vashti being killed
בא שטן וריקד ביניהן והרג את ושתי
The simple reading of the Megillah indicates nothing supernatural about Vashti's downfall. Rather, it seemed to come about as a result of a drunken kings demands, and the queens refusal to acquiesce.
However, it is also possible that the author of this passage had in mind the Midrash about Vashti being made miraculously ugly, leading her to refuse to appear (cf. Megillah 12b). If that were the case, this would be an example of a miraculous event being the act of Satan, although the Talmud doesn't use the term "ma'aseh Satan" to refer to this act of Satan. Significantly, in this case, unlike the above usages of the term "ma'aseh Satan" Satan isn't depicted as causing sin, but rather other problems.