What causes speaker cone to extend when...

Recently I made two changes to my audio system and each time I noticed the speaker cones made several large extensions while playing music before settling down (that is, the whole cone moved in and out from the rubber surrounds). It was almost like they had a hiccup. The music was playing and everything sounded OK. The first time was when I disconnected my speaker cables from the amp - everything was turned off by the way - and replaced with new cables. The second time was when I disconnected my turntable, made some changes, then plugged it in again, along with new phono interconnects.

I was wondering what could cause such a reaction; e.g., could it be new voltages moving through the system?
Does it happen with any other source?
I gave away my Thorens turntable many years ago because of that problem and others. I will admit though it was because of the record being warped or an off center spindle hole.
There might have been enough stored in the caps in the first case if they moved when unplugged. There is sometimes some very low material that is not musical; I have notices this on a CD as well. Some kind of artifact from the recording process is my best guess. I can't explain some of the weird things MY system does so this is the best I can do on yours.
This only happened when I first started listening to music after making the changes. After a few moments the speakers settled into their normal "duty" and didn't go through the "hiccups" again.
What kind of amp and Preamp do you have? It sounds like a DC issue - either the amp or Preamp has a temporary issue with DC offset, which gets through for a few seconds before coupling caps or a DC servo circuit compensates. I wonder if you turned on the components in a different sequence from usual?
Both the preamp and amp use vacuum tubes (the amp also has a tube rectifier). The preamp phono stage is a Tetra circuit by John Broskie with an Aikido line stage also by Broskie. The amp is a Bob Latino Dynaco-clone ST-120.

I don't think I turned on the components in a different order.
I think Stanwal was right about the stored energy. I had this happen to me when a friend brought over an old Marantz integrated and when I connected the speaker wires, the cones moved so much I thought they'd jump out of the cabinet. I've never experienced that before and it was unnerving, to say the least, but I kept my best face on and listened to the Marantz all the while dying to take it out of my system.