Power several 12 V @ 1A Pumps

I’d like to power several 12 V @ 1A pumps, which will be turning on and off sporadically. Sometimes they will all be running at the same time, and sometimes only one pump will be running.

I’m assuming it’s okay to use a 12V at 5A adaptor?

No idea, you haven't provided a link to the datasheet for your pumps.

Datasheet here: https://www.sparkfun.com/datasheets/Robotics/Other/spec%20sheet.jpeg

The startup current of a brushed DC motor is typically 5-10x the running current, which must be taken into account.

So the worst that could happen is they won't all be able to start up at the same time?

Until you know the details of the current draw, you can only guess. The power supply could shut down (perhaps cyclically), blow a fuse, etc.

Brayd: Datasheet here: https://www.sparkfun.com/datasheets/Robotics/Other/spec%20sheet.jpeg

Alas nothing like enough information in that.

You will need to measure the winding resistance - take a multimeter in resistance mode and measure the resistance across the terminals. Also measure the resistance of the leads shorted together (the pump resistance is the difference of these figures).

From the winding resistance the stall current can be estimated as V/R, V being the supply voltage.

That tells you the current each pump can pull at startup.

However its not totally clear if the pump is using a standard DC motor (it does look like it from the illustration though).