Only tested on a Mac with 1Password 7 using Agile Bits' sync.
If you have shared and private vaults on 1Password, using the Generate Password button in 1Password Mini doesn't let you select which vault that password should be saved in until it becomes a login, however, at that point it has already saved the password you generated in your shared vault, and anyone who you share that vault with can see both the password, and the site that it was generated for. This has obvious security implications but also, maybe less obviously, privacy implications as you may not want your entire company to know that you just generated a password for a jobs site.