Ok,
lets do a quick worked example to see if we are on the same mind set here.
The original post stated it was a Steye TMP, with some mods from Arsenal.
Core rules has the Steyr listed as no recoil comp, but as this is what the topic is mainly about, lets assume he somehow managed to make up 3 points of recoil comp.
Now, for a one gun, one hand example.
1st Simple action, fires long burst.
Recoil from 6 bullet long burst, first action, would be -5 to shooter. The 3 points of RC would drop the penalty to -2 dp, so first long burst would be rolled at -2 dp.
Now we know that the Steyr CAN'T fire a second long burst with the second simple action,
this is a limitation of the weapon itself, only a HVAR can do that, but lets ignore that for right now as we are currently working on recoil part of the equation, so...
2nd simple action, fire 'another' long burst
Recoil carried over from first simple action of -2 is still present, and since all of the weapons RC has been used up, all of the recoil from the second long burst, -6 for six bullets, has to be added, giving a total recoil of -8 for the second long burst.
Ok, now lets assume that the shooter is going to try the same, but this time (s)he is firing with a modified Steyr (RC 3) in both hands, and has ambidexterity, so will not be suffering a penalty for firing off handed.
1st simple action, same as first example, -5 recoil, 3 of it taken by the modified RC, leaving -2 dp left over.
2nd simple action, fire a long burst with the second weapon. Now since the not being able to fire two long bursts in a action is a limitation of the weapon itself, and because the second weapon hasn't fired at all this IP, the second weapon CAN fire its long burst.
The shooter is already at -2 dp because of uncompensated recoil from the first shot. His body is shaking about due to the uncompensated recoil from the first shot. It doesn't matter how much RC the second weapon has, even if it had 20 or 30, his body has already taken uncompensated recoil from the first burst, his body is moving about and making it harder to shoot straight, and the RC of the second gun can have NO effect on this.
So, the 3 RC for the second gun CAN reduce the -6 recoil from firing a second action long burst on the second weapon, therefore the -6 will be reduced by 3, making it -3. You then add the already uncompensated recoil from the first shot (-2), for a total of -5 dp to the second shot.
Therefore he has (RAW as far as I can tell) reduced the recoil on the second shot by 3 points, the RC of our modified Steyr.
This is how I see it happening.
So 'my' summary,
1: He can fire two long bursts, because it is a limitation on most (ie non HVAR) weapons not to be able to do this, a mechanical limitation of weapons, not a limitation of the rules, and as he is firing the long bursts on different weapons, neither of the weapons are firing two long bursts on the same IP.
2: She gets the RC for each pistol, but the RC of the second pistol only reduces the recoil
caused by the second weapon, it can not reduce the uncompensated recoil from the first weapon.
This second point is important, because instead of firing a long burst with A and a long burst with B, if she decided to fire a long burst with A, and only a single shot with B, even though the weapon has 3 RC, and a single shot as the second simple action only cause -1 point of recoil, the other -2 points of RC from the gun can not compensate for the -2 uncompensated recoil from the first shot, ie example 3...
Simple Action 1, long burst, -5 recoil, 3 points of recoil taken by pistol, uncompensated recoil, -2 dp to first shot,
Simple Action 2, single shot with second pistol, -1 recoil for single shot as second action, completely compensated by second pistols RC 3, but second shot still has -2 dp due to the -2 uncompensated recoil from first shot, which is now moving around the body, and the second weapons RC can do nothing about it at this stage.
Just how I see it, examples help.
Sorry it is slightly long winded, it is 3am, and I really need to go to bed now

Nite all.
Max,
Dunedin, NZ