From your own link:
The first thing to know (which might put you somewhat at ease) is that these card readers do not store any of your details on the device itself. Whenever you slip in your card or punch in your PIN, you can rest assured knowing that the reader isn't holding onto any of that.
This is good news for those worried about mobile online banking. Basically, by requiring a card reader for certain actions, you're forced to carry that card reader around with you if you ever want to perform those actions while on the go.
Some card readers are universal, meaning they can read and generate codes for any EMV card, as long as the card is compatible with the reader's online bank. So in that sense, you could use someone else's card reader when necessary, and their reader wouldn't store anything about your account or card.