"Alarm people" (like most "network people" and "phone people") only deal with low voltage. For liability and licensing reasons they are not going to wire up directly to an AC line like to the receptacles in your picture.
That leaves two likely possibilities:
A plug-in power supply which converts 120V AC to low-voltage AC or DC. That is by far the most common in my experience, because it allows the alarm company to replace the power supply very quickly if needed - unplug from receptacle, move two wires to the new power supply, plug it in.
A transformer similar to those used for thermostats and doorbells (and now for door cameras). This is a much more permanent style of installation. It is typically done by installing the transformer into a knockout on the side of a metal junction box in an area where access to the wires is easy.
Extremely common for thermostats because they are normally installed (initially at least) by HVAC people who have to deal with 120V anyway so an extra junction box with permanent wiring is no big deal.
Extremely common for doorbells because doorbells normally sit for many years, are often installed as part of the initial build (as with HVAC/thermostats) and cheap plug-in wall warts were not as common many, many years ago and not as reliable as a simple 120V -> 16V (or whatever) transformer.
Less common for alarms because the alarm people (a) are normally adding an entirely new system - most houses aren't built wired for alarms like they are for HVAC or doorbells, and (b) they are not normally trained/licensed to work with 120V AC, and installing a transformer on a junction box is technically outside their capabilities, and (c) they are often working entirely in finished areas where a plug-in power supply will look much better than a transformer on the front of a box and a transformer on the side of a box only works in unfinished areas because it has to be accessible.
So there is a small possibility that if you trace out the power wires you will find a transformer hidden away. More likely is that you will find a plug-in power supply in an unexpected place. Either way, disconnect it and you are done. But do not simply disconnect at the alarm panel because then you are leaving a power source running with nothing attached, which is a potential hazard.