By quickly modifying the shape of the effective potential of a double SQUID flux qubit from a single-well to a double-well condition, we experimentally observe an anomalous behavior, namely an alternance of resonance peaks, in the probability to find the qubit in a given flux state. The occurrence of Landau-Zener transitions as well as resonant tunneling between degenerate levels in the two wells may be invoked to partially justify the experimental results. A quantum simulation of the time evolution of the system indeed suggests that the observed anomalous behavior can be imputable to quantum coherence effects. The interplay among all these mechanisms has a practical implication for quantum computing purposes, giving a direct measurement of the limits on the sweeping rates possible for a correct manipulation of the qubit state by means of fast flux pulses, avoiding transitions to non-computational states.