This is an interesting mechanical problem. I'll begin by discussing the basic rule idea. I was about to quote the FATE rules on extras, but BESW's answer does it for me, and the basic idea is spot-on. All stormers (which in FATE is everyone with Fate points) should have the "Possibility-rated" extra, for free, granting a two-box Reality stress track and the ability to learn Reality.
(Make sure to use a variant in which FATE points belong to individual opponents, not to "GM-controlled NPCs" as a whole - Torg needs that.)
Now we can answer your question. The approach depends in part on your design goal:
Mechanical Balance: matching Torg
To reproduce the mechanical effect of the original Torg rules as closely as possible, then go ahead and let the Reality skill grant additional stress boxes.
This does make the Reality skill significantly more effective than intended for combat skills by the FATE designers, but that's consistent with Torg. The truth is that this imbalance will matter most in combat between stormers and ords. Since ords tend to transform or... well... explode when attacked with Reality, combat will inevitably stack in favour of stormers whether you grant them additional stress boxes or not. Especially since ords, in keeping with the design goals of both systems, shouldn't have Fate points.
This choice also creates a stronger difference in Reality skill level between stormers. But that's no bad thing if you're trying to reproduce the mechanical effect of the Torg rules. Reality was a distinguishing skill in Torg.
(A reality-focussed character in Torg rules can mop the floor with just about any other character, unless they're from the same reality to start with. Assuming they don't mind blowing the neighbourhood apart with a giant storm every time they fight.)
I'd even suggest that ords also have zero Reality stress, but instead move straight to consequences. (Seems harsh? It is, but in Torg, ords don't resist Possibility energy well. That's what makes them ords. How long do you want them to sit there taking damage in a fight they're bound to lose?) If you don't want this, give everyone a Reality stress track, and limit the Possibility-rated extra to granting the Reality skill.
But in Torg, Reality didn't attack your health so much as your Possibilities. The direct way to move that to FATE would be to let Reality stress either depend on total Refresh or steal Fate points... both of which are very bad ideas* that will break the FATE dynamic.
On the other hand... Torg is the first step on the path that lead to FATE. Player control of narrative and introduction of subplots, plot manipulation points, multiple interweaving realities on a common skill-based mechanic... I've argued before that Torg is FATE's founding father.
So what if your design goal is:
If we use FATE to match the story function of Reality duels in Torg, then we need a more nuanced approach. Because there is a key difference, important to the setting of Torg, between Reality-based consequences and standard FATE combat consequences.
Reality duels tend to mess up the surrounding environment.
So here's a full pass at FATE-based reality, with some sub-options:
All characters have (as an aspect) a "Home Reality".
(Depending on your aspect handling, this may be an additional Aspect in itself, or part of everyone's Concept aspect. I actually recommend the former, but the latter has more flavour.)
Everyone gets the standard two Reality stress boxes.
Characters with positive Refresh (and hence Fate points) are stormers; others are ords.
(Take a look at the way Dresden Files handles gaining monstrous powers and being a PC/NPC for a good look at how to handle the dichotomy.)
Only stormers can learn Reality.
Beginning a Reality duel costs a Fate point. Once spent, Reality attacks may be made against the target for the rest of the scene.
(The character is consciously invoking a reality storm here, for Heketon's sake.)
Reality attacks are made directly against Reality stress, and cannot be made against people who have the same Home Reality aspect that you do.
Use the Collateral Consequences rules (FATE System Toolkit, p61.) To quote the most relevant part...
The players can also make use of three communal consequences, one of each degree of severity... Players can effectively use them to offload harm from themselves onto the world around them.
Now we're talking. It's in keeping with Torg to allow Collateral Consequences for Reality track damage alone. (These consequences will normally take the form of "storm damage", of course.) In a Reality duel, both combatants will feed the building storm... until one of them has nowhere to offload the energy and gets Taken Out.
Being Taken Out on the Reality track represents transforming.
The character's Home Reality aspect is replaced with "Transformed: (attacker's reality)". (If they're an ord and were already transformed, this is the point where they get Taken Out in the form of a big fireball instead.)
This is, of course, a wonderful character opportunity to declare changes to other aspects suitable to the character's new reality... and lasting injuries should consist of being ill-adapted to their new mindset until the player's had a chance to move skill points to match.