Is there a way to set a default Vault for my searches

When you say that they have "separate" vaults, do you mean that you share vaults with each of them, or that they each have Private a vault (which they should by default)?
In the former case, these are your vaults, so an account-wide search will show results from all your vaults. In the latter case, you should never see any results from their Private vaults.

In the application, the top search bar with the "Search in [Your account name]" text is the account-wide search. If you want to search a single vault, then in the middle pane to the right of the All Categories drop-down, there is a magnifying glass with lines on the left which has hover text "Find in Private" or "Find in" the name of your selected vault.
In the plugin, the search bar with the "Search in [Your account name]" is the account-wide search. If you want to search a single vault, then click the account name in the top left corner for a drop-down menu from which you can select a vault. You should see the search text change to "Search in [vault name]".