The multiple and very extended triaxial strongly deformed bands of the 163,165Lu nuclei are used to ascertain the spin dependence of the odd quasiparticle alignment. The band heads are found to favor a tilted alignment geometry which gradually evolves into a transverse configuration. Distinct dynamical regimes are thus identified in specific bands and spin intervals, which are discussed in terms of wobbling excitations based on the analysis of the wave functions and E2 transition probabilities.