Which Siri on which device does what?
I know if I ask Siri to set a timer, my phone will set the timer.

I'm assuming that you have &quot;Hey Siri&quot; enabled because I do this many times per day.

But, why not the iPad?

The iPad is fully capable of setting a timer via Siri.  I just set one on my iPad by invoking Siri with the home button.  It's also capable of doing so via &quot;Hey Siri&quot; as well. If yours isn't doing so - either via &quot;Hey Siri&quot; or manually, I suggest we look at this in another question, because that in and of itself is a technical issue.

If I ask Siri to open Google Chrome, which is on all three devices, which device responds?

I actually tested this.  Siri opens on the device that responds first.  Putting my iPhone next to my iPad and saying &quot;Hey Siri&quot; both devices responded however, it was always my iPhone that took control becuase it had the Siri &quot;tone&quot; first.  When that tone sounded, Siri on my iPad closed.  For the record, Handoff and Continuity was enabled.
For some reason, I don't have &quot;Hey Siri&quot; on my iMac with Catalina (10.15.5).  I can only invoke it by clicking the Siri icon or pressing the hot key assigned.  However, I would assume it functions in the same manner.
As for putting a priority on the device, decide which one you want to respond to &quot;Hey Siri&quot; enabled on one device and not on the others.  It's easy to invoke.  I have mine on my phone since I use it to control Apple Home (my lights, fans, etc.).  I don't enabled Hey Siri everywhere to avoid confusing things.