Q: Log in via "Back to my Mac" from outside my home network

You should be able to using the correct user name/password.

Back to My Mac - Use

Back to My Mac Screen Sharing

Back to My Mac Troubleshooting

Because iMac admin account A has established Back-to-My-Mac via iCloud the "Entire" Mac is now accessible from outside your home by you Macbook Air which is using the same iCloud account.  iCloud is providing visibility of the iMac to the Macbook Air.  Once you connect you will be able enter the username and password for either account A or account B from your Macbook Air.

Thanka Bob, but would user iMac(B) be notified? or can they keep working on iMac(B) without noticing?

User B does not appear to receive any notifications nor menu bar indications that another user on the Mac is also logged in.

I am currently using my Macbook Pro logged in as Me, and I have another Mac using a Screen Sharing session to a different account on my Macbook Pro, and there is no indication that the other account is active, unless I go digging.  I know I can see another user logged in if I use the 'who' command in a Terminal session.  I'm sure there are other ways.

However, you would have to know to look, and I cannot see anything telling my normal account that the other account is logged in.

NOTE:  If I do not intentionally log out of the other account when I stop screen sharing, the account is still active on the Mac.  If I wish to shutdown all the apps running in the other account after I'm down with the screen sharing session, I have to use log out of the account before disconnecting, OR I have to use Fast User Switching from my normal account to switch to the other account and log it out.

I'm not going to log out of my normal session just to find out.  Sorry.

But I'm sure you can run that experiment yourself.

Perfect, that sorts all my doubts. Say neither iMac A and iMac B are not logged in and you log in remotely iMac A, what happens on the screen? Can anybody standing in front of the machine see what you're seeing while sharing?

I got mixed results.  I do NOT know if the mixed results was because the client Mac was running Snow Leopard (10.6 - major release ago), but here is what happened.

When logged out of all users on my Mavericks (10.9) Macbook Pro, then started screen sharing from my Snow Leopard Mac to the Macbook Pro, it logged in as the primary user controlling the Macbook Pro screen and keyboard (anyone able to see my Macbook Pro would see what I was doing from remote).

So that no one would see what I was doing, I would need to first remotely login to the normal user account (maybe start the screen saver so that the screen/keyboard are locked from passer-by's), then start a new screen sharing session to the "Other" account, and now that account will start up in the background.

NOTE:  If I logged into the "Other" account first, then used "Fast User Switching" to move the display away from Other to the normal account, then start a new screen sharing session to get back to "Other", when I tried to logout of Other, it put a dialog box on the Fast User Switched to Normal user's display asking if I really want to close all applciations.

That is to say, the normal message Other should have received, was instead delivered to the physical display which is currently displaying the Normal user's account.

Again, I do not know if this Fast User Switching behavior was because my client Mac was a 10.6, or if it is just the way it is.  I do not have a newer client Mac I can connect to my Mavericks Macbook Pro to give that a try.

So I would say, if no one is logged into your iMac, you first login to the normal account, force the screen saver to start, then disconnect the screen sharing session, and start a new session to your Other account.  That way you can login/logout without the normal users noticing.

It does not matter.  First one to login is the one that has the physical screen.

If it makes you happy, then think of normal as admin, and think of Other as the one you do not want to be seen by the account controlling the screen.