I think maybe it doesn't need to do this incrementally as you type, but if you hit return it should open the hierarchy selectively.

Once have confirmed your search item, it should offer forward/backward arrows and display how many matches it found.

The reason I don't think it should be have incrementally like browser ^F is that you might wind up opening hierarchy that you didn't intend, during a typo. Maybe it could be incremental if it closes hierarchy when you delete text, but it might be complicated to remember what was manually opened already. So I think it's simipler if it waits for you to hit 'return',