Uh, I guess you need to switch your account first before updating, or buying all apps you have bought in old account again in this new account so that you can update them accordingly.
To put stuff a bit clearer, since I also use multiple account configuration, and all of them are active, here is my solution to update apps from multiple accounts (and from multiple countries of course):
When I receive app updates:
1. In my main store account: update as usual.
2. In my secondary store account: dismiss all popups requesting for password on that account as it will eventually not work. Then go to "iTunes and App Store " setting, swap account, then update again.
When I switched my account, I bought all free apps I have bought and rest in my iTunes app library using new account again. For paid app, as long as I could buy it using main account, I would not mind a lot.
I believe you will feel confusing upon reading. I am sorry about it but this is better for me to tell you what I have experienced.
Here is my original case.
I had one account, and switched to different countries from time to time and buy apps/music at that country. One day then, Apple required all users switching country need to provide valid credit card info before switching. I then experienced a hard time since I was not at the country where I bought some key apps, and eventually I could not solve the problem myself to switch the country.
I then sought to multiple account setting. First problem was to update all apps bought in that country using my main account. The second problem was all songs bought at that country. For free app, I just bought them again. For music, I could only hope all music was downloaded and properly stored locally, since I couldn't spend once more for the same song.
I would feel glad if you could actually finish reading all of them and hope it could help.