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Motivated by the intriguing possibilities of steering ultrafast non-adiabatic processes through the geometric properties of bands in quantum materials by laser pulses, we extend a wave-packet transport theory, previously well-established in the adiabatic regime that intuitively captured geometric properties of bands, to the transient and non-adiabatic regime. This extension facilitates us to investigate macroscopic ways of manifesting microscopic band-geometric effects that highlight the special capability of non-adiabatic drivings not available to adiabatic drivings. These include imprinting band-geometric properties to the current rate after switching off the laser pulses and the induction of intrinsic macroscopic spin polarisation with an orientation not accessible by adiabatic processes. In particular, the microscopic geometrically-rooted intrinsic spin coherence is shown to underlie the spin-mediated parts of the macroscopic photocurrents. Through explicit calculations of an example with Rashba spin-orbit coupling, the spin-mediated part is shown to be discernible from the non-spin-mediated part in terms of the anisotropy of the photocurrents. Working principles behind the above theoretical results allegedly applicable beyond the Rashba example are distilled to inspect experimental data collected for SnSe, exhibiting considerable anisotropic effects. Consistency between theory and experiment is observed, paving the way of further exploration into the above intended direction.