From what’s my experience each voice has its own LFOs. The only thing that’s special about a paraphonic track is that the LFOs of more than one voice gets influenced by the trigs. But when the trigs doesn’t sync LFOs their phase can be all over the place.
About the issue at hand: let’s have a little thought experience to understand especially free running LFOs better.
When a free running LFO (which is bound to a physical voice) gets started by, for example, the very first trigger and no other follow up triggers change its mode it will run and run and run, no matter if the sequencer itself is running or stopped. It just does its thing with its phase constantly circling.
Now suppose that this physical voice comes across a single plock which changes the lfo temporarily to a synced mode. When the lfo afterwards continues in free running mode its phase got also altered/synced.
The above mentioned plock doesn’t need to be a real plock, a sound lock with synced lfo settings will also result in that alteration/syncing of the phase.
The same holds true when the physical voice gets temporary borrowed by a paraphonic track. This also can and will influence the phase of a free running LFO.
When trying to simulate a (what you think is) “buggy behavior” from an init sound you’ll need to take all of this into account. When starting out with just a single voice in use on a init sound everything is simple and predictable, but as soon as the configuration gets more “real-worldly” the phase of free running LFOs can get influenced in so many ways that it becomes mind-boggling to try to predict it.
Conclusion: IMHO what you experience isn’t a bug. It’s just the nature of free running LFOs. Unless you enforce very carefully some syncing by your own their phase is somewhat “unpredictable/random/all over the place” (decide yourself how to name it ).
Manually switching the LFO mode to trig mode and back temporary syncs them, of course.
(Disclaimer: I’m quite in a hurry, so my explanations above may be a bit “off” in the details, but the picture itself should be correct / no time for dedicated testing)