There are a few ways a video generating device can lock to or interpret an external source. The video inputs on video synthesizers such as LZX Vidiot, and the LZX Expedition modular system (including the Visual Cortex module) include broadcast sync generators so they are capable of generating a video signal autonomously. As a result, their inputs try to genlock onto the external signal’s timing while keeping their own outputs very stable and consistent. When your input source comes from a device with erratic sync timings, the video synthesizer devices refuse to match their timing and this is what creates the behavior you’re seeing.
Due to the nature of VHS tapes as a playback medium, timing will always be inconsistent as the play head reads the signal off of the magnetic tape. Older tapes or older VCRs will make the timing even more erratic. You don’t notice this on most displays because the display is simply responding to the unstable timing.
To use your VHS tapes with your video synthesizer, you will need a device called a Time Base Corrector (TBC) between the VCR and the video synthesizer input. Some VCRs even have TBCs built in, and these would be ideal for your application, and likely give you a better quality image as well.