Lusche is right about your position when you recenter but there could be another problem which has been discussed on the TIR BB. It's difficult to explain but I'll give it a shot.
There are two types of motion for TIR with vector expansion (VE). The basic is rotation. That's what lets you turn your head and "look". Look left, look up, look right, etc. Your virtual head stays where it's at and the view just pivots from there (this is what you get without VE). This would be the same as sitting still and just looking around with your eyes and turning your head.
There's another type of motion though called "translation" which is added with VE. Translation is a linear motion (left/right, up/down, fore/aft) as if you're leaning. For instance lean forward and your virtual head moves closer to the instrument panel. Sit up higher and your virtual head moves straight up, slouch and it moves down. So, in addition to rotation, you now have a virtual body that can lean and twist which means you can lean to the side to look around a canopy bow or the headrest. Make sense?
The problem some people have been having is that the translations aren't correct. It seems that in some cases the translation axis (up/down, slide left/right, fore/aft) are not always aligned with the direction of your view, instead they are relative to the centerline of the aircraft. If aligned with the direction of your view then no matter what direction you're looking the translations always work the same. Look at your 9 o'clock and lean forward and your virtual head moves in the direction you're looking and closer to the canopy side glass. Look out your six and slide to the right and your virtual head slides to the right.
This is always the way it's worked for me since I first started using TIR but some people have complained that their translations are backwards when looking out their six. What happens is the translation axis are fixed as though you're always looking directly ahead, even if you're looking at your 9 o'clock or 6 o'clock. Look to your 9 and lean forward and instead of your head getting closer to the side of the canopy it slides to the right, toward the nose just as if you're looking and leaning toward the nose. Look at your six o'clock and you're seeing nothing but headrest. Slide to your right and your view moves to the left on screen (of course this is to the airplane's right side). Move your head back, away from the headrest, and your view actually moves closer to the headrest since TIR is seeing "back" as toward the tail of the plane.
I can't explain how people with the same TIR and TIR software have this issue unless it's in whatever way a particular game treats TIR. This sounds like what you're seeing. You're looking at your six and seeing nothing but headrest so the natural impulse is to move your head back away from the headrest but instead it goes the opposite direction. If your translation axis are dorked up then doing what Lusche ways will only make this worse since your resting head position is toward the back of the cockpit and closer to the headrest.
HT has a feature called "TrackIR Object Relative Move". This is under "Options/Preferences/View Options". I cannot use this feature as it screws up the translation axis for my setup so I leave it off. All of my views operate correctly this way. My guess is you have it selected on but in any case change whatever you have. If the option is selected in your menu than deselect it. If it's not selected then go ahead and select it. If either of these corrects the problem then recenter as Lusche describes and you'll be in good shape.
One of the reasons I went into such detail is that there is a lot of misunderstanding about the problem, hopefully I was pretty clear as to what might be happening to you and why. If it doesn't help then I'd recommend you go to the Naturalpoint BB. They're pretty helpful and can sort things out for you or recommend you exchange your TIR.
As far as the other problem you have you may really have had a software issue that screwed everything up. If so, I'd recommend uninstalling TIR and reinstalling the latest software from NaturalPoint (it's version 4.1.028). MAKE SURE YOU DON'T USE 4.1.029, it's an alpha version of the next software and will really screw you up. If it still happens again it might only be a bit of TIR confusion so try recentering. I know when I first started I had something similiar to what you describe a couple of times and I thought everything was AFU but just needed to recenter. When first starting up you always have to recenter, otherwise your "centered" view can be in any direction.