I may be venturing into conspiracy theory territory here, but stay with me...My understanding was it was a distribution deal only.
RTD wanting to do a soft reboot at the same time could very easily be understandable after so many fans dropped off under Capaldi/Whittaker.
There's what people/companies say in public, and what they really do. The two are rarely the same.
The BBC (including RTD) were always going to say "Disney's money is going to help us make Doctor Who better, but they're not going to have any creative control". That's the public image. They know that there will always be a fear that a Disneyfied Doctor Who won't be the same as the Doctor Who we've come to know & love over the last 60 years. They are desperate to allay those fears, to avoid losing fans of the show.
However, money talks. It always has, and it always will. The reality is that Disney definitely do have the ability to influence creative decisions. Influence is not the same as "Control", in that the final decisions will always be made by the BBC - but the BBC would definitely take Disney's requests into account.
I think it's quite reasonable to see the Space Babies episode as being heavily influenced by Disney's desire to appeal to their Nickelodeon audience.