  The electromagnetic character of the $\Delta I=1$ transitions connecting the
one- to zero-phonon and the two- to one-phonon wobbling bands should be
dominated by an $E2$ component, due to the collective motion of the entire
nuclear charge. In the present work it is shown, based on combined angular
correlation and linear polarization measurements, that the mixing ratios of all
analyzed connecting transitions between low-lying bands in $^{135}$Pr
interpreted as zero-, one-, and two-phonon wobbling bands, have absolute values
smaller than one. This indicates predominant $M1$ magnetic character, which is
incompatible with the proposed wobbling nature. All experimental observables
are instead in good agreement with quasiparticle-plus-triaxial-rotor model
calculations, which describe the bands as resulting from a rapid re-alignment
of the total angular momentum from the short to the intermediate nuclear axis.
