I'm having the exact same issue and have found a fix for now.
- Open Parallels.
- On the top menu bar, select "Configure..." under "Virtual Machines"
- A window will popup. Select "Applications" under Options
- Deselect the checkboxes "Share Windows applications..." and "Share Mac applications..." shown here: cl.ly/image/2d0G2Q2w082L
It may work with just one of the options deselected, but I haven't tried. Hope there's a better fix for this
UPDATE: So after a few times of ST2 opening the correct browser, I reset the options in Parallels (Both share application are now checked), and it still works. Looks like ST2 will "remember" after a few times.