What can cause a lab DC power supply to become an AC power supply?
There is a reasonable possibility you made a simple error. Many bench power supplies provide +/- dc outputs but also have an earth connection. The earth connection is of course earth BUT, the power supply's dc outputs may well be isolated from this earth stud/socket. Many power supplies are configured like this.

What you might have done is connect the scope between earth and Vdc outputs and seen an ac waveform and then connected your meter (on dc because you mentioned + and - voltages) to the correct points and seen the correct dc voltages.

It's too much of a coincidence that your power supply was set to +/-10V and your meter measured +/- 10V for it to be some obscure earth fault or power supply fault. I'd re-check if I were you.

Why would you see an ac waveform on your scope? The power supply outputs were floating wrt earth and connecting anything to the probe would produce ac mains voltages on the display - touching the probe with your fingers would do the same.