Can connecting of AC adaptor first into device, then into mains pose a risk of voltage spike?
Are both connecting orders equally safe in these terms?


Depending on the equipment, in some cases the answer is no, the connecting orders are not necessarily equally safe, and the order can definitely matter. There is a reason why you found that "Manuals of several various electronic devices I came across recommend connecting their AC adaptor first into the device, then into mains."

During my research some years ago, the main issue I found is the LC-induced voltage spike, generated by the combination of the inductance of a typical switch-mode PSU's output filter and the cable going to the power supply "brick" (L) and the low ESR of (especially) ceramic input capacitors in the equipment (C).

Linear Technology have AppNote 88 which explains this better than I could write in a few paragraphs - "Ceramic Input Capacitors Can Cause Overvoltage Transients".

In brief, the problem is that the already established voltage (e.g. 24 V in the Linear AppNote) is applied across an uncharged ceramic capacitor in the equipment (a simulated notebook PC power input circuit in the AppNote). In this situation, the capacitor has had no chance to (comparatively) slowly charge as the PSU voltage ramped-up, with the cable attached to the equipment, which would have happened in the "recommended" connection sequence. Instead it sees a step-change in input voltage when the PSU cable is attached. The result can be a voltage peak exceeding twice the input voltage. To quote from the AppNote:

"The input voltage transient problem is related to the powerup sequence. If the wall adapter is plugged into an AC outlet and powered up first, plugging the wall adapter output into a portable device can cause input voltage transients that could damage the DC/DC converters inside the device."

Another article with experiments which show the problem (although here they use a switch on a PCB at the end of a long cable to the PSU, rather than plugging-in a connector) is here by Pololu - "Understanding Destructive LC Voltage Spikes"



Summary - Unless there are any device-specific instructions to the contrary, it is less risky to connect the (unpowered) AC adapter first into the device, then into the mains, as you saw in those instruction manuals.