You didn't specify platform here. If you're experiencing this problem on the PC, the easiest way to go is to google the appropriate console commands to adjust the affinity with your companion. But when you're on another platform, such as the X1 and PS4, the problem has to be resolved with normal in-game methods, and that's what I'll cover here.
I am going to make the broad assumption here that you have narrowed the problem down to Synth Instigators because you've actually killed a hostile settler and found Synth Components when you looted their body. If this is so, then the problem should be treated in two parts.
First, go to your Red Rocket settlement. You will immediately be confronted with:
- Generation 2 Synths, your regular but upgraded plastic covered synths
- Hostile Settlers, your generation 3 synth instigators that look like humans
- Neutral Settlers, the human settlers that will aid the settlement's defense
- Your hostile craftable companion, a super-buff custom made automatron that you love dearly
- Your settlement's defense system
Second, since the Generation 2 synths will be easy to see and distinguish from settlers, dispatch of them first. If you are worried about killing settlers, or otherwise causing them to be hostile by accidentally shooting them in the mix, then allow your defense systems to dispatch of the synths. Alternatively, you could lure the Generation 2 synths to an open area where you feel more comfortable with dispatching them.
Third, locate your hostile settlers (or your synth instigators) and kill them. They are easy to distinguish from neutral settlers in that their name directly above their head will be red, and neutral settlers will be attacking them. As with the second step, be careful not to hit neutral settlers in the crossfire or it will complicate the situation. Once you have killed the synth instigator, confirm that the synth instigator was a synth by looting their body and finding the Synth Components.
Please note: If you see only hostile settlers, and no other neutral settlers assisting in the defense of your settlement, and up until now and have not seen any Generation 2 synths, then this is not a synth instigator issue and must be addressed by the "waiting" method of fast traveling away from the settlement, and waiting for a period of 2-3 days before returning.
Fourth, deal with the companion problem. Hopefully, up until this point, you will not have engaged your craftable companion. Do not attack or hit them during your crossfire. You must escape the area, obtain the appropriate distance between yourself and your hostile companion, and then fast travel to another settlement. Once you get there, wait a period of 2-3 in-game days or simply play the game for the same amount of time without returning to the settlement, your choice.
At this point, you should be able to return to the settlement. Both your companion and your settlers should have their hostility reset to neutral. If not, you either did not wait the appropriate amount of time, or this is bug-related and there's nothing that I could further suggest besides resorting to a previous save.
And last, in regards to perks, from the Fallout Wiki on Intimidation (here):
The Intimidation perk only works on raiders, gunners,
and Gen 3 Synths.
Of course the caveat is that it's not guaranteed to work, the enemy must be lower in level to you, and if you fail the intimidation interaction, they can become hostile. I think the worst part here is that:
Hostile companions can not be pacified.
So it seems that any pacification-based techniques are not going to work on a companion, and an Automatron is considered a craftable companion.
Finally, if this really is a bug that is somehow related to the settlement itself, and hostility of your companion is not a result of your craftable companion hating you... then it may be worth noting that it is possible to un-align and re-align yourself with a settlement and that should reset its hostility towards you. One way would be to complete a BOS radiant quest found on the airship. It will require you to convince the affected settlement to donate crops to the BOS. When you complete the mission, it will destroy the alliance you have with that settlement, and return their status to independent or not allied. In doing so, your craftable companion will likely return to the settlement that it was at previously. You can then complete the corresponding Minutemen quest to ally the settlement with you which basically reset the hostility of that particular settlement towards you. It is WAY more work than the steps outlined above because the settlements are chosen at random for the BOS and Minuteman quests, and are chosen from any settlements that are not allied with either. Again, that is assuming that the companion somehow received its hostility from a bug residing in that settlement.