a likely explanation is as follows.
The stainless steel sink is not as thermally conductive as most other metals in the kitchen, and it does expand when heated. So if you place something hot on it, it gets hot right at the contact point and quickly expands by a thousandth of an inch or so, right under the contact point, before that heat has a chance to be dissipated away into the rest of the sink.
since the bottom of the sink is slightly curved, this expansion will slightly tip the pan sideways, moving the contact point to the side and thereby heating a different patch of the sink. the center of mass of the pot is raised by the tipping and it would like to rock back to its equilibrium point, which process is aided by heating a new contact patch of the sink, and the pan rocks back, overshoots, and the process continues.
Note here that the heat transfer between the lip of the hot pan and the contact patch in the sink depends on how long the pan lip is in contact with a given patch of the sink; this contact time is a maximum when the pan is tipped over to its maximum deflection, and it is then that the sink kicks the pan.
This means that the intermittent rocking force is exciting the natural resonant frequency of the pan which sets it into the rocking motion. Since there is very little damping in the system, it will rock as long as the aluminum pan is hot and the sink is cold.
You can demonstrate this yourself by putting a cool pan in the sink and setting it into rocking resonance by hand and noting the frequency. you will find it is the same as the resonance excited by the hot pan rocking on a cold sink surface.