This happens when you forget to add a ‘lytic after the regulator, although the datasheet only shows a 100nF on the output. Not that it really matters on this case. On the pulse generator the logic gates are fed from a regulated supply, mostly so I can forget and use the same as the output stage. Without load and having only a 100nF ceramic halfway between the 7805 and the 4093 (less than a cm…) the rail bounces about 300mVp-p, but it becomes negligible when using a small 10uF in parallel.

Just for kicks I removed the ceramic cap, leaving the output without bypassing at all. The result was a set of narrower 800mVp-p spikes that settled quite fast.