No, the weapon-launched-PCO will not know what the team the "firing" weapon is on. It can't know it.
You have to look at 5), there's a line with
This single line define what team object the template will spawn.
Only control points are capable of passing on their Team value to attached spawners. As the weapon-launched spawners are not actually attached or related to the soldier who fired them, but are created completely independent, they are not bound to any team (which would default them to Team 0). And the line of code above is a method to define a default team for an ObjectTemplate. You can set this line for Templates attached to flags as well, but they will have no effect there, as this setting is immediately being overwritten by the flag's team value.
You also want to make sure that on 4), you set the
to what you need. Also, if you want multiple selectable points or want to use them for both teams simultaneously, make sure to set up a unique Spawngroup for each set. Spawngroups define (as one could guess) which individual spawnpoints should be grouped together. On most vanilla maps, all spawnpoints are attached to a single flag, which practically only means that all of them get assigned the same Spawngroup (This is what BC42 does by default). This results in a single selectable spawn position on the ingame map, located at the centroid of all individual spawnpoints.
In my example, I specified a single group for all the 4 or 5 individual spawners spread around my rallye point, so they also only get a single dot ingame. If you'd use the same group for other spawners (or if you just place multiple instances of the rally points throughout the map, without letting them expire), all of those will be combined ingame into a single dot that will be seen somewhere in the center of the map. If you choose to spawn on this point, you will randomly spawn at one of the individual spawners with that ID. If one team should get multiple pickup-kits that have this spawn-gun (as I propose in the thread), you should make individual weapons for each of them. If you want to add this spawn-weapon to the generic kit selection menu (so a large number of possible players have it), I would suggest you take a look at RandomGeometries, which would allow you to easily make sure that the players get unique spawners. Or at least you could cycle easily through a large number of individual groups which would make it very unlikely that the same ID is used simultaneously by two players. It's important to note that "RandomGeometries" is not actually random, but just iterates. So it starts with geometry 0, then 1, 2,3,... . Which also has some nice benefits, just as it does in this case.
I hope this makes things clearer and doesn't confuse you even more

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EDIT:
@Black Mamba: If you have no meaningful contributions, just refrain from posting. There's been a noteable increase in troll and flame posts from your end, and we don't intend to tolerate this much longer. It might be mildly funny once, but definitely not in these quantities. It's plain immature and annoying.