It sounds to me like you want to be able to access each of the remote computers without them being able to access yours.
Pretty basic setup, you need to assign a personal password on each of the OTHER computers.( you can use the same one if you want for each)
you want t initially log into their computer using the ID then give you and the random password it generates.
using thre connection you have made, open the teamviewer window on their machine by clicking the TV icon, it will open a window.
navigate to Extras > Options.
Now, go to the Security tab and change the password under ‘Permanent Password for Unattended access’.
enter the password twice.
Below that look for "rules for connection to this computer" /windows logon choose "allowed for all users" form the drop down.
Click "Ok"
Do this for each of the computers you want to control, keep track of the Teamviewer ID?password you chose.
when you are done assigning passwords:
On your end all you need then is the teamviewer ID and the password you set up as noted above.
On your computer open Teamviewer, click on computer and contacts in the lower right of the teamviewer screen and add their system( you will have to create an account for yourself to log in).
You can add their computer and password by clicking on the little icon of a person with a + sign and choose "add remote computer" once you are done( choose an alias also to identify them..IE "mom") anycompuetr the is online will appear in the list when you sign on.
just choose and identity, double click and it will log in.
They will not be able to access your system.
Let us know how this works or if there is an issue.