When you login using the same account on another PC, it re-asks your account info on all the other PCs you're logged in.

We were, and still are, connected on the same wifi network / router
Using the old launcher, the "Java" launcher:
My brother and I used to play using the same account- (Not at the same time)- We only put the Email and password once on the laptop and once on the Desktop PC. On Desktop pc and playing multiplayer I would quit the game and then, my brother would simply open the launcher from his laptop and play on the same server, WITHOUT putting the login information again. When he was done I could simply open the launcher on the Desktop PC again and play. No re-entering your account info was required

When I installed the new launcher on the desktop PC it needed login info. After I put the login info a play multiplayer on that very same server again.. When I was done playing, I closed the launcher and my brother opened the new launcher on the laptop. It needed login info there,too.
I entered the the email and the password and he started playing. After he was done I opened the new Launcher on the Desktop PC and saw it needed login info again.. after I put it, I open the launcher at the laptop only to see that it needed email and password there, again..!
It's pretty annoying having to re-enter the email and password again and again everytime someone uses the same account. On the old launcher you could play using the same account on like 5+ computers as long as they were connected on the same Network/ router
Also, noboby else than me has the login info