If I clearly understand, anyone who has a wifi access point can get connection history of any device that connect to it.
You have misunderstood. This article discusses companies that essentially run WiFi "as a service" for multiple clients (e.g. KFC restaurants, as mentioned in the article). These routers run common software and are manged by the same company. Because of this, that company can note when your device comes within range of any of its routers, e.g. by using your device's unique identification (MAC address). This does not require you to actually make an authenticated connection to these routers. Because the company knows where its routers are, it can therefore make a record of when your device comes into range of them: a patchy record of your time/location history. (If you're worried about it: turn off WiFi at all times when not in a trusted place, such as home and work. You could also lie when giving away personal information to things such as free WiFi providers, if they insist on such information for service.)
If I am connected to my router with my device A at home, am I able to check my device's connections to other WiFi in the past ?
Your router at home is not run by one of these companies. Your router does not know what other routers the devices on its network have been connected to in the past. Therefore you cannot use your router to inspect your device's previous connections to other routers. (If you simply want to track its location over time, use GPS.)
Your device, however, probably does have a record of the routers it has established connections to. This is how it remembers to reconnect, e.g. to your work or café WiFi each time you visit. But it wouldn't note the routers' physical locations, and it wouldn't share this information with every other router.