It is up to you and your DM, but likely it would be controlled.
Iron Defender (UA 11-12):
By 3rd level, the tinkering in your free time has borne you a faithful
companion, an iron defender. This metallic creature resembles a hound,
a cougar, a bear, or another four-legged creature of your choice. It
is friendly to you and your companions, and it obeys your commands.
The Iron Defender has an INT of 4. The Dragon Talk: Sage Advice on Mounted Combat admits that this is vaguely defined, so rule at your discretion. According to Jeremy Crawford, most players make the choices for their mount if it isn't an important NPC-tool of the DM.
Mounted Combat and Controlling a Mount (PHB 198):
A willing creature that is at least one size larger than you and that
has an appropriate anatomy can serve as a mount
While you're mounted, you have two options. You can either control the
mount or allow it to act independently. Intelligent creatures, such as
dragons, act independently.
The anatomy is suitable as it resembles a four-legged creature of your choice (Gnomes are size Small see PHB 37, Iron Defenders are size medium, see UA 11) and the creature is willing (see first quote).
I would rule that the Iron Defender is not an independent creature because it already moves on your initiative and enacts most of the benefits of a controlled mount:
In combat, the iron defender shares your initiative count, but it
takes its turn immediately after yours. It can move and use its
reaction on its own, but the only action it takes on its turn is the
Dodge action, unless you take a bonus action on your turn to command
it to take one of the actions in its stat block or the Dash,
Disengage, or Help action.
This is congruent with what a controlled mount does.
The initiative of a controlled mount changes to match yours when you
mount it. It moves as you direct it, and it has only three action
options: Dash, Disengage, and Dodge. A controlled mount can move and
act even on the turn that you mount it.
As you have noted, it's unclear. That means it's DM's call.
There are a large number of points in the rules of 5e that are not entirely clear. It is explicitly intended that the DM adjudicate those things at their table. It's just one of the features of the game system - they're actively encouraging table adjudications and houserules.
That having been said...
This is in a published book. We can make a reasonable assumption that the wording is as intended... and the wording doesn't say. If we look at the rules for Bardic Inspiration, we see the following (emphasis mine):
Once within the next 10 minutes, the creature can roll the die and add
the number rolled to one ability check, attack roll, or saving throw
it makes. The creature can wait until after it rolls the d20 before
deciding to use the Bardic Inspiration die, but must decide before the
DM says whether the roll succeeds or fails. Once the Bardic
Inspiration die is rolled, it is lost. A creature can have only one
Bardic Inspiration die at a time.
The wording here states outright that in this particular case, the player must decide before the DM says whether the roll succeeds or fails. By implication, then, that's not inherent in the fact that it's giving a bonus to the roll.
As such, it should be possible to give a bonus to a roll after success or failure has been determined - and, indeed, the Divine Soul sorcerer's Favored by the Gods feature (XGtE, p. 50) does this - and Flash of Genius leaves activation in the hands of the player.
Thus, it would make sense that the player could wait until after success or failure had been declared before deciding whether or not to use Flash of Genius.
eidt: and, we now have new information... sort of. The Sage Advice Compendium offers a not-entirely-clear clarification to go with the above.
You use Flash of Genius immediately after the triggering d20 is
rolled and before any of the effects of the roll are applied.
Unless a rule tells you otherwise, a reaction occurs immediately
after its trigger
So... it's after the roll, but before the effects are applied. Yes, that seems to cover both of the previously described options. Admittedly, it does tend to nudge it closer to the "probably before success/failure is declared" side of things, but to my eyes it's still firmly within DM adjudication land.
Best Answer
Just one of its attacks
Going by the wording used in the quote you provided, all of the language used to describe the chosen creature's attack is singular:
It appears as though, RAW, it only imposes disadvantage against one attack roll. This is also consistent with similar features, such as the Protection fighting style, which uses similar wording:
Although you include the quote that it can "use its reaction on its own", remember that all creatures only have one reaction (unless explicitly stated otherwise), so the Steel Defender would only be able to use its Deflect Attack reaction once per round, and it would only regain the use of its reaction at the start of its next turn.