I thought it was a bug when I first discovered it. The makers of the VSTs do not seem to. The problem exists over lots of plugins and companies. When the device is tempo sync'd and the tempo changes it either mutes quickly and comes back at the new tempo or it pops and clicks as it jumps to the new tempo. The result sounds awful (see examples above).
But I think it's kind-of a limitation of the delays. If I could imagine how it might work, I would basically create a new VST instance at the new tempo, fade out the old one and fade in the new one. Then the results of the two delays would merge together at the new tempo. This wouldn't be a big deal if tempo changes were infrequent. When they are , it could create a garbage collection issue if not a memory issue. Also, melting the two delays together at varying tempos could sound goofy too.
I'm not sure there is a perfect way to handle it. The most important thing is to recognize it.
5 years ago, I thought it would be great to create tight tempo maps of my projects (and I regularly did). I did this largely for the purpose of adding tempo sync'd delays but also for adding synth work.
I have since really stopped doing this. I now just measure the projects tempo roughly at a high point in the project and use that tempo for tempo sync'd delays.