I thought about this a little. Seeing the number of alien operations and the attack pattern, the nations might have founded PHALANX as a secret special operations organization anyway, assuming, that the aliens do not really invade, and the armies can't deal with alien operations because of the asymmetry of operations.
The aliens operate in small groups (like special ops) but with a fire power of small armies, when on ground, and they are quite hard to attack in open air for early stopping them. And an attacking army (which could certainly bring them down after some experience collected at their first attacks) would just make them start their ships and bombard the troops.
So the nations have founded a special ops organization, to fit exactly to the thread. And they do it secretly because it looks a) better if the people think the own countries troops can handle the situation and they can show their independence. But in the course of the game, OF COURSE every country tries to have a insurance if PHALANX can't handle the job. While the best are working for PHALANX they are not better than every other guys together.
I expect the countries to deploy their own anti alien forces, develop special tools and weaponary and so on. If you do your job good, these national organizations will cooperate, the countries will support you not only with money, but with their specialized gear, as well as surveillance. If you are just ok, you may operate in parallel to the nations affords, and if you do bad... well then in concurrence. If you LOOSE a country (that then is allied with the aliens), well be prepared that your stations are not only attacked by the aliens but also by the nations troops (which surly overrun it if you are still a secret organization), and may even lead to open war between the countries.
As long as the aliens are only explorers or experimenters, PHALANX may be the only player - and founding cutting just comes from being doubtful that the PHALANX can do the job (and it is better to throw the money in the national project) At the time, the aliens prepare for war, the foundings will stay up on PHALANX, but also the national organizations will be founded well, and then a dropping of funding clearly is caused by alien operation. At the time the first military ufos arrive, I'd expect national figther groups in the sky (where maybe 10 could shoot down an ufo at 50%, but the nations will have the numbers) and special ops troops on the ground on the maps to collect the ufo.
Countries who decide you are not welcome (without alien influence) may force you to close down or hand over your bases (for a compensation) and don't allow ground missions (or even shouting down ufos).
At the time, the aliens start to install bases on earth, (and the only will in secret remote areas or in allied countries) there might be aggressive civilians and opposing military on the field WITH ALIEN TECH ENHANCED WEAPONS designed for human servants (which might give total new strings of optimization techs etc...). Your bases then might have to be defended by well armed conventional army, against conventional military forces, and your base defense must bring ufos down before the cand bombard those troops, which still will not protect you from defending your base against opposing military special ops and alien special ops.
So:
First part of the game (secret special ops): Funds are increased with success, and decreased with fails.
Second part of the game (alien warfare): Funds are increased by success and cooperation with the country (exchanging tech, selling ufos, buying special gear), and decreased on fails and alien influence.
Third part of the game (total warfare): Funds depend on how much the war against aliened nations costs, and if PHALANX do its part on fighting the alien supporters (while still bring down alien ops in the free countries), so that PHALANX partly operate as special ops team for the free countries, destroying allien bases before enemy military can reach the base up to execute brain washed politicans. At this part, PHALANX surely have developed its own secret service to have such missions also in "friendly" countries, before they turn sides.
If you are successful in being a secret organization, in the first place, the aliens would think SOME kind of problem happened on the planet, but bringing in stronger gear might only bring greater loss (perhaps the aliens assume, that a big part of the population is capable of bringing them down, though the experiments don't show how that is possible, making them careful because of the hidden enemy or unknown conditions). If you are not careful, the aliens will be early aware that there is only a small troop, that can just be overrun with stronger weapons. On the other hand, if you are not successful in bringing down the aliens, they might belief that there is no reason for stronger gear. If you do you things "loud" like put no efforts get you out of public awareness, then the aliens will gear up fast.
In the second part, your job is to carefully operate with your friends to help them stay happy, for example give outdated tech to them, sell ufos, and so on, to arm your friends up, but not to the scale that they become a thread, when turning sides.
Ind the third part, the aliens have allies. Disturbing the enemy alliance by bringing down support ships and raid alien bases on enemy ground, as well as annihilate brainwashed key politicians or military commanders, you force the enemy to stabilize their bridgehead, so that this takes pressure from you and your allies, so that the country can be freed from alien influence by your operations, or by conventional military operation of your allies, where the first option of course lead to more funds.
I really like to see that every country has its own search tree (some quite different, some quite similar) and the aliens their own for your human servants, and if you are to slow with yours, they will outsmart yours, but they start later AND you are in the position to combine every gear, tactics, information, and so on, which will give you an advantage.
Something like sending your soldiers to a special ops anti alien training of allies for a month. Or use special armor science Russia gave to you, because PHALANX are so good friends :-)