From thermodynamical consideration, rather a monotonically increasing crystal growth velocity with increasing undercooling is expected in the crystallization of liquids, mixtures, and alloys [P.K. Galenko and D. Jou, Physics Reports 818 (2019) 1]. By contrast to this general theoretical statement, Al-rich Al-Ni alloys show an anomalous solidification behavior: the solid-liquid interface velocity slows down as the undercooling increases [R. Lengsdorf, D. Holland-Moritz, D. M. Herlach, Scripta Materialia 62 (2010) 365]. It is also found that besides the anomalous growth behaviour, changes in the shape of the recalescence front as the growth front morphology occur. In the light of recent measurements in microgravity with an Al-25at.% Ni alloy sample onboard the International Space Station (ISS) results confirming this anomalous behavior as an unexpected trend in solidification kinetics are presented. The measurements show multiple nucleation events forming the growth front, a mechanism that has been observed for the first time in Al-Ni alloys [D. Herlach et al., Physical Review Materials 3 (2019) 073402; M. Reinartz et al. JOM 74 (2022) 2420] and summarized with detailed analysis in the present publication over a wider range of concentrations. Particularly, the experimental measurements and obtained data directly demonstrate that the growth front does thus not consist of dendrite tips (as in usual rapid solidifying samples), but of newly forming nuclei propagating along the sample surface in a coordinated manner. Theoretical analysis on intensive nucleation ahead of crystal growth front is made using the previously developed model [D.V. Alexandrov, Journal of Physics A: Mathematical and Theoretical 50 (2017) 345101]. Using equations of this model, quantitative calculations confirm the interpretation of experimentally observed propagation of the recalescence front and obtained data on the microstructure of droplets solidified in electromagnetic levitation facility (EML) on the Ground, under reduced gravity during parabolic flights, and in microgravity conditions onboard the ISS.