FFT returns large low-frequency power - probably because signal is interpreted as containing cycles that do not fit. How is this called?
Your reasoning sounds correct. It is impossible to see from your example what frequency that low frequency is.

If the frequency of the phenomenon is 0 Hz, then it is simply a direct current (DC) bias that affects the first bin of the discrete Fourier transform (DFT). If none of your signal of interest is in that bin then you can simply ignore it in your analyses or set it to zero. If your signal never goes to negative values, then you have DC bias (although there could be other low frequencies).