The reason not all wired remote shutter releases are universal, regardless of whether they do or do not have built-in timers, is that not all cameras have the same size/shape connecting plug to attach them to the camera.

The controller you linked to above gets around this by supplying a plethora of adapters to fit just about any camera currently on the consumer market. Almost every camera with a port for a wired remote only needs two commands from the wired remote: a half press and a full press. The rest of the timer's work regarding when the signal is sent is done in the remote itself. The shutter speed, aperture, ISO, focus mode, etc. is still set via the camera's menu just as if you were using the camera's built in shutter button (If the shutter speed is set to Bulb in-camera, then the length of the signal from the remote will determine how long the shutter stays open, exactly the same as how long you hold the shutter button down would if you were using the camera's built-in shutter button).

I've used a similar timer with a permanent Canon N3 connector several times over about three years (make that almost seven years as of late 2017 - it's still working just fine) and been very happy with it. The only external difference appears to be the shape of the end of the cable that hooks to the camera. Ignore the complaints in reviews on sites such as amazon.com about having to remove the batteries from such timers because you can't turn them off. They are like a digital watch: as long as the alarm isn't constantly beeping the batteries will last for years. In the case of the remote, be sure it is not running/counting down and actively trying to trigger the shutter periodically when you store it.

I suspect the low-level protocols for Canon and Nikon would differ as well. Even if one managed to hook up a remote for one brand, it is unlikely it would be capable of sending the correct encoded commands for the other brand.

They all have three wires. One is a ground, the other two are simple electrical circuits to complete that carry one-bit of data: open or closed. One is for the half press, the other is for the full press. There are no further 'protocols'. There are no 'encoded' commands. It's like a light switch, either electricity is flowing or it is not. The current is supplied by the camera, the remote is only a passive switch with two positions (three if you count the unpressed position when both circuits are open).

The key is to make sure the right wire from the remote is connected to the right wire in the camera. Thus the need for various adapters, so that the ground is connected to the ground, the half-press wire is connected to the half-press terminal on the camera, and the full press wire is connected to the full press terminal.

Panasonic does use a single wire plus ground to signal both a half and full press by placing resistors of different values in the circuit depending on the switch position. Everything you ever wanted to know about remote cable release connections.