I notice how everyone here is commenting that they did a search on one device and then a little later did a search from another one.
This is not an apples for apples comparison, and if one of my employees came to me and said that's how they did a data test in a live system with consistently changing data I would tell them to go back again and redo the test.
I just did a test on a few different devices and on several different browsers and different IP's, and the answer is that each device (mobile and PC) and each browser returned the exact same set of information.
Why is that you ask? Well in each case the tests was done within a few seconds of each other. I tried this on both QF and VA and got the exact same results.
Later this year I'm taking the family away on a holiday, when I was doing the bookings I did a few dummy bookings to try and find suitable flights. On a couple I got as far as the entering payment screen. Qantas sent across a few emails stating that they had put the tickets on hold for me for a couple of hours in case I wanted to complete the payment. No doubt during those couple of hours it would have had an effect on other peoples search results, and may have made the price temporarily go up.
Whilst I'm not sure if VA do the same thing, it wouldn't surprise me if they did.
A few posts back, one member suggested that they use all sorts of metric to determine how likely you are to buy. I'm going to tentatively call BS on that, I did a look at QF's website and did a dummy booking with developer tools running. I hooked into the DOM events. All the events I saw had to do with displaying and hiding visual popups. The only reason I'm going to say tentative rather than outright is that all source files where minified which does make understanding them more difficult. I would strongly suspect that the airlines have used things like heat maps to work out where on their website peoples eyes might be drawn and how people may interact with a checkbox (yes it's no accident that certain check-boxes required you to un-select them), but this would be something done at design time, not in production. Admittedly I only did this with Qantas, so there may be other sites out there which do this monitoring, of course with the web being increasingly used via touch devices there is no longer the mouse interaction which such technologies would be reliant on. There is also the risk with such timing checks that a less than great connection affects the timings and even other (IT or non-IT) distractions.
As for incognito mode, this is often called "cough" mode, since it prevents a snooping spouse from easily seeing what you where doing on a computer, it prevents entries in the computers history, cookies and offline files being permanently saved, however it does nothing to prevent external websites from tracking whom you are and where you've been. Websites do not typically detect incognito mode running (although there is ways of doing so if you're so inclined)