From my perspective, my ideal escorts (oh my~

) are the ones ensuring I do nothing. They pamper me and take care of my needs. I don't have to fight. I don't have to ink. I only have to run and swim to my heart's content, as far as possible, and little else. Teammates that accomplish this, even if it's just for one brief moment or only during the clutch when we finally get our crud together, I adore. And thus I try to do the same for any teammate that picks up the rainmaker.
When creating turf for your carrier, revert back to your turf war roots and ink like a n00b! Sling ink everywhere, as far as you can, however you can! Clever, experienced, and desperate carriers will be on the lookout for even the smallest drop of good ink in the most random and out of reach places then use it to propel them a little further. So use your kit to benefit them in whatever way possible, especially if you have a bubbler, kraken, inkzooka, or even bomb rush—just go ahead and tap "C'mon!/To Me!" and they should be able to take the hint and be ready for you to activate it.
Given that, your rainmaker bearer has a mind of their own. They will zig when you zag. They will ignore a path you lined with splash walls and instead crawl over glass and open concrete in squid form. They may notice something is up with a route you chose, or not, and go an entirely different direction. They may be standing in one spot plotting a brilliant strategy they're waiting to draft you in or just scratching their butt with the rainmaker. Get use to it...
But be willing to take a bullet for them and hope for the best while you respawn. Minding that, do not stick too close to the rainmaker bearer. Better one of you get splatted than both simultaneously. This will also keep you from blocking each other's shots or view. And keeping your distance also allows you to better react and scan your surroundings more clearly, because the most upsetting turnovers begin to happen when the bearer is waylaid from behind, the sides, below, and above. Also, distancing yourself just enough can get you ignored by the other team. Many wind up getting tunnel vision and reveal themselves as they chase or cutoff the rainmaker. Their greed or desperation makes them oblivious to your presence and vulnerable to pick off.
But when your carrier goes splat, decide if you want to move out in front to defend the bubble or fall back. If you fall back, flank and pick off your opponents as they reveal their locations when they attempt to pop the bubble.
I'm certain I'm forgetting a few things, and this is only based on my solo queue play, but I'm sure others will chime in with useful knowledge I've overlooked to share or have yet to encounter.