In the lower plot image, if you are referring to the collection of orange asterisks before the start of the variable section (for want of a better way to describe it), the ‘spurious’ data could represent noise. In addition to 'MinProminence', setting 'ProminenceWindow' could be an option. Another option would be various approaches to filtering to elinminate the high-frequency noise, if that is the problem. (Start that approach by calculating the one-sided Fourier transform to see if there is band-limited high-frequency noise that could be filtered. Then design a frequency-selective lowpass filter using that information.)
It would help to have the data to experiment with. Without it, I can only speculate as to what the problem is, assuming that I even understand your question correctly.
