Pretty sure vi does not care about, or is even able to detect, the difference between a middle-mouse and a shift-insert paste.

As mentioned elsewhere, if your vim is compiled with clipboard support(:version and look for +clipboard), you can copy/paste from the clipboard.

* is the Linux selection register.

+ is your clipboard.

So yanking is just set paste, "+y or " * y, set nopaste. Similarly you can do a "+d in vim and ctrl-v it in your browser or anywhere you can access the clipboard. You can " * d/" * y and paste it with your middle mouse button.

The mouse has nothing to do with it...

If you paste method doesn't let vim know what's going on, use pastetoggle, otherwise don't.

Or you can use shift+insert.