Said power is "stretching his mind to touch yours" and "grow clones of his mind inside others' brains"... now, human mind being information, it is evidently susceptible to The Drummer power, and his distorted informational space could disrupt a floating mind tentacle as much as it disrupted Suskind's cybernetic link to the goggles.
- We have no hint that Dowling's power works on Century Babies, and more than one that it doesn't (he would have had no need to brainwash Snow if he could have just deposed one of his mind clones in Snow's brain, and we have no real clues about Stone being compromised either).
- Now, there is also a very good reason why Dowling would hesitate before using his power: unless otherwise constrained, the created mind clone could very well decide that he does want to be the big boss and going on to overthrow original Dowling, once he started diverging significantly. Given this consideration, and Dowling's own arrogance, it comes as no surprise that he didn't try immediately to overtake The Drummer's brain... That is, believing it was possible for Dowling to tamper with The Drummer's mind, as such a brain is probably even more impervious to Dowling's power than a normal Century Baby.
Admittedly, all of this takes a lot of fridge brilliance...
Think about it. Why does he even argue with the other members of the Four ever? Why didn't he stretch his mind into the Planetary team, Anna Hark or the City Zero survivors and their children? Because he couldn't! It is doubtful that the paranoid immortal superhumans from that alternate Earth would have ever allowed someone with a power like Dowling's to exist if it posed any threat to them at all! They almost certainly scanned the Four after they passed through the transformation device to see what the end result was. If any of the Four possessed an unacceptably dangerous power then they would have blown that space capsule to bits. Instead they allowed them to leave. So Dowling's power allowed him to stretch his mind into ordinary humans (probably the people that worked to build all of the Four's massive bases and vehicles), but he could never control superhumans, although he might imply that he could as a threat.
The whole cross-over directs us over the whole history of the Dark Knight: the gun-toting Golden-Age Bill Finger design, the silly Adam West incarnation, the Darker and Edgier Neal Adams of the 70s, the Frank Miller Dark-Age Old Knight, and the Modern-Age fighting-Jakita-first, ask-questions-later one.
But at the end, we get the Planetary version, which represents an amalgam (no, not that Amalgam) of all the other versions, and explains in two pages how his origin really makes what he is: someone who will honor his parents' memory above all else, and someone trying to save people. You could draw a parallel to what Grant Morrison did with his "Doomed planet. Desperate scientists. Last hope. Kindly couple." and the general tone of All-Star Superman.