No, FM3145 says ATC built that Addhara factory . . but it is a non-issue really since BT has always been hazy on ruler/corp boundaries, and tend to wave them away. If the Caeser had not wanted them to build a new plant it would not have happened. In fact the sentence before in FM3145 it talks about the Hegemony investing in ATC to replace losses. My use of 'Hegemony' in that sentence was in regards the a wholistic entity.
There is a difference between capacity and actual production- they CAN make 10 CN9-H a month, but they decide to only make 1 CN9-H a month to keep the factory running as an example. It would be a lot easier to hide a increase in capacity from any Republic diplomatic station than it would be to hide the actual production of more mechs/tanks/etc a month. This is important b/c the Marians would have a mission to Galatea (which has to be allowed b/c the Republic's laws) buying salvage from mercs. FM3145 actually hints at this since with the League's reformation in '39 Ignatius ordered increased production to boost the HAF.
Actually, Ignatius is not doing what his father and grandfather did- instead of trying to take military control, he is trying diplomatic and cultural ties with unaffiliated worlds in a effort to expand the sphere of influence. It also clearly states (stil FM3145 pg 185) Ignatius has refrained form military expansion- which would be the policy from '28 until the '40s. The construction of a mech & veh production facility in '99 is a pretty clear indicator of Cassius military expansion policy (along with where he died) while Ignatius did not increase military production for 7 years after the Black Out. Ignatius is also the Caeser that ordered the inclusion (as paying customers) for non-MH applicants to their war college as a means of culturally aligning those allies who had attendees. Only when he learned the League had reformed (and could no longer play off the proto-states) did he expand production facilities.
Here I agree in part, and in part not, Ignatius is different in terms of cultural assimilation, but, the expansion of Factories is something that seems to follow the path of his grandfather and great-grandfather, when building the Factory in Illyria, although If we are guided by the shattered Fortress Ignatius was rearming the V Legio and the authors dismembered it again to give him something to destroy the Camacho Cavaliers, the same with the others, but it caught my attention that green troops were sent to the front line in an insane maneuver taking into account that the Field Manual 3145 itself said that the troops and commanders of the MHAF were the most veteran of the periphery, which does not close by any side that is if and send those troops to the combat front when they should have been in Pompeii burning training tanks and doing war games with some merc unit, not be in Maximilian to be exterminated but hey
Regarding factories and states, the authors are diffuse when they want and when they want they are not in their definitions
As for the production rates, this is on account of the order to replace equipment in the different units, nobody commits suicide by making a low production so as not to replace the units lost by your troops and mercs
Even if you have the most efficient mech / tank / aero collection office in the universe in Galatea, you are not going to chain yourself and depend exclusively on that, nor on the salvage that you raise in each battle or on what you have saved that you could find.
Your production is the first thing to take into account and I do not see any Cesar count the last to his production
Remember that even CGL did not elaborate on anything about what all the Marian factories produce, neither those of Hadrian nor those of Marian Arms, we know nothing about them after the introduction of the Marauder in Horatius, neither Hadrian nor Marian arms did anything to respond to the economic advance of ATC? I really doubt it