If you have dangerous, timed Sequences, it might be very traditional but also frustrating if the Player can die and and old Savegame must be reloaded -- if your Game has Autosaves or the Player cannot die anyway, then it is no Problem anyway. But watch out that whatever the Player has to quickly do is in any Case something simple and obvious, or else the Sequence may become unnecessarily infuriating.
As for Minigames, on one Hand the Player may think "I didn't sign up for this!" every Time a Minigame pops up, but then again I intend to insert Minigames into my Game, for which I initially did not want any Minigames, because I think they are a good Way to to bring in some refreshing Change in the Gameplay from Time to Time. Walking around to talk in Multiple Choice Dialogues and combining Items can get a little tiring after a While, and then I actually quite welcome a little Minigame.
However, because of the very "I didn't sign up for this!"-Aspect, you may consider to make the Minigames skippable. This may be either entirely functional (press little X-Icon and it is simply solved), or be explained in the Game's Narration: In my Case, there is a Sequence where an Engineer inspects a Machine you give him and it spontaneously falls apart, so he asks you to help him to reassemble it, which you either do or you skip the Minigame, and then the Engineer will be like "oh well, I am sure I can get this done on my own...", followed by the classical "Three Hours Later..." and voila, it is solved -- it is basically "Narrative Cosmetics" and requires only a few Lines of Text.
If your Action- or Minigame Sequence requires alternative Controls, like Cursor Keys instead of Mouse Controls, make sure to mention this, like using a quick Tutorial-Text. In such Cases, always try to additionally offer a Way to control the Sequence with the Mouse as well.