The tempo envelope doesn't follow the defaults for the automation envelopes (probably since it isn't a real "automation" envelope, and it doesn't have Bézier and the other fancy curves), so you have to set the tempo envelope's default shape separately: Right-click on the tempo envelope -> Envelope defaults.
If you want to make the tempo change gradually rather than all at once, you can do this by double clicking a point on the tempo envelope and checking the box "gradually transition tempo to next marker." This will make it behave like a linear point in a normal envelope.
Apologies, even though I'd set all my points to linear after creation. I think that they were causing my new points to be square because they were created square.
If I delete all points and create new ones I see they are all linear now.