Pair MFi hearing aids with multiple devices

I am trying my first pair of MFi hearing aids. I paired them to an iPhone and an iPad. I notice they don't show up in the list of bluetooth devices. But, they do pair with both and can (somewhat) hand off. I can look at one device and see if the hearing aids are connected to it or the other device. I can make adjustments from either device, so that is nice.

But, to use the manufacturer app, the device needs to be connected to the device where I run the app (usually the iPhone). So, if it is connected to the wrong device, I can momentarily stream and the iPhone/iPad switch the connectivity and then I am set.

Problem is, it almost always connects to my iPad when I first turn them on. And that is almost always the wrong device (I carry my phone). Is there a way to influence this connection. I assume the hearing aids can't do that, but maybe the iOS devices can agree which gets priority if they are both present.

Would the order in which I paired the devices affect the order of connection? Is it random? Something else?