Hi there!
I'm 100% sure Resolume supports this... but I've had a lot of trouble making sure that my clip playhead is in sync with BPM-synced effects.
When I play a clip with random playback, and set the interval to the same as random playback effects, they are not in sync. (See how the playheads don't move at the same time here.)
There is a setting called 'start settings' on each effect parameter, where there are two options – 'clip trigger' and 'BPM phase lock'. That sounds very promising and very sync'y! But neither puts the effect in sync with the timeline!
So I poked around some more – it looks like the combination "beat snap –> 1/4" + effects set to "clip trigger" is the closest I get to the effect being in sync. The problem is... it only works sometimes! At the same time 'clip trigger' is not the default start setting, so I've got a long day's work ahead of me changing all my random effect presets to use 'clip trigger' instead of the default. And even then I can't expect that the effects will always be in sync with the timeline.
I've been using Resolume for many years, but I somehow never understood how these various settings interact – what blindingly obvious setting/concept/idea am I missing here? I can't be the only person who has tried to match random timeline movements with random effects movements...?